DCN - Stage2 Analyses

CFA, SEM, EFA and LSEM Analyses

by Michael Demidenko

RMSEA .35 SRMR .20 TLI .06 CI .12

# color palate for site related plotting
pal<- c("#1D91C0","#67001F","#CB181D","#78C679","#F46D43","#F7FCFD",
                 "#A6CEE3","#FD8D3C","#A6D854","#D4B9DA","#6A51A3",
                 "#7F0000","#D9D9D9","#FFF7BC","#000000","#F0F0F0",
                 "#C7EAE5","#003C30","#F16913","#FFF7FB","#8C6BB1",
                 "#C7E9B4","#762A83","#FC9272","#DF65B0","#EF3B2C",
                 "#74C476","#E5F5F9","#AE017E","#F7F7F7")

1 Project Description

This project is based on the Stage 1 registered report submitted at Developmental Cognitive Neuroscience (Demidenko et al 2022). The proposal is to use a sub-sample of the full Year 2 (follow-up to baseline) ABCD sample. This includes 1000 participants for the initial analysis and a held out 1000 participants for the follow-up LSEM/EFA model.

This html document and .rmd was last ran using the platform: x86_64-apple-darwin17.0 version: rsession_info\(session_info\)R.version$version.string` on November 2023 by Michael Demidenko.

2 Load Data

Importing the final data for the ABCD, AHRB and MLS data. Three variable lists are created:

• mod_vars: ROIs/Contrasts specified in the a prior model/used for CFA, these are used for subsetting for plotting and ESEM
• nacc_pairs: ROIs/contrasts subset for NACC to evaluates distribution and plots between variables
• insula_pairs: ROIs/contrasts subset for Insula to evaluate distribution and plots between variables

The subjects for each sample are loaded and variable names are relabeled to match stage 1 code. Note, the mean signal intensity values from python are floats, so they continue until the 9/10th decimal place. This level of precision is not necessary for mean signal intesity values and lavaan encounters errors with these values when trying to fit models. So we round them to the third decimal place.

#Variables used in CFA model, reformat so bileral and runs and similar contrast next to eachother
mod_vars = c(
  # Approach
  # nacc
  "AWin_v_Neut_L_NAc_r1", "AWin_v_Neut_R_NAc_r1",
  "AWin_v_Neut_L_NAc_r2", "AWin_v_Neut_R_NAc_r2",
  "BWin_v_Neut_L_NAc_r1", "BWin_v_Neut_R_NAc_r1",
  "BWin_v_Neut_L_NAc_r2", "BWin_v_Neut_R_NAc_r2",
  "BWin_v_BLose_L_NAc_r1", "BWin_v_BLose_R_NAc_r1",
  "BWin_v_BLose_L_NAc_r2", "BWin_v_BLose_R_NAc_r2",
  # insula
  "AWin_v_Neut_R_Ins_r1", "AWin_v_Neut_R_Ins_r2",
  "BWin_v_Neut_R_Ins_r1","BWin_v_Neut_R_Ins_r2",
  # avoid 
  # insula
  "ALose_v_Neut_L_Ins_r1", "ALose_v_Neut_R_Ins_r1",
  "ALose_v_Neut_L_Ins_r2", "ALose_v_Neut_R_Ins_r2",
  "BLose_v_Neut_L_Ins_r1", "BLose_v_Neut_R_Ins_r1",
  "BLose_v_Neut_L_Ins_r2", "BLose_v_Neut_R_Ins_r2",
  "BLose_v_BWin_L_Ins_r1", "BLose_v_BWin_R_Ins_r1",
  "BLose_v_BWin_L_Ins_r2", "BLose_v_BWin_R_Ins_r2"
)

# for pair plots: NAcc ROIs & Insula ROIs

nacc_pairs = c("AWin_v_Neut_L_NAc_r1", "AWin_v_Neut_R_NAc_r1",
             "AWin_v_Neut_L_NAc_r2", "AWin_v_Neut_R_NAc_r2",
             "BWin_v_Neut_L_NAc_r1", "BWin_v_Neut_R_NAc_r1",
             "BWin_v_Neut_L_NAc_r2", "BWin_v_Neut_R_NAc_r2",
             "BWin_v_BLose_L_NAc_r1", "BWin_v_BLose_R_NAc_r1",
             "BWin_v_BLose_L_NAc_r2", "BWin_v_BLose_R_NAc_r2"
)

insula_pairs = c("AWin_v_Neut_R_Ins_r1", "AWin_v_Neut_R_Ins_r2",
             "BWin_v_Neut_R_Ins_r1","BWin_v_Neut_R_Ins_r2",
             "ALose_v_Neut_L_Ins_r1", "ALose_v_Neut_R_Ins_r1",
             "ALose_v_Neut_L_Ins_r2", "ALose_v_Neut_R_Ins_r2",
             "BLose_v_Neut_L_Ins_r1", "BLose_v_Neut_R_Ins_r1",
             "BLose_v_Neut_L_Ins_r2", "BLose_v_Neut_R_Ins_r2",
             "BLose_v_BWin_L_Ins_r1", "BLose_v_BWin_R_Ins_r1",
             "BLose_v_BWin_L_Ins_r2", "BLose_v_BWin_R_Ins_r2"
)

2.1 ABCD

Load ABCD data

abcd_id_include = read.csv("../output/ABCD/abcd_final_subjs.tsv", sep = "\t", header = FALSE) 
colnames(abcd_id_include) = c("subject","subsample")

abcd_include_first = abcd_id_include[abcd_id_include$subsample == "First_1k",]
abcd_include_second  = abcd_id_include[abcd_id_include$subsample == "Second_1k",]
#abcd_include_um = abcd_id_include[abcd_id_include$subsample == "UM_Only",]

abcd_roi_sig = read.csv("../output/ABCD/region_roi-meansignal.csv", sep = ",", header = TRUE) 
abcd_roi_sig$subject = abcd_roi_sig$subj %>% gsub("sub-","",.)
abcd_roi_sig = rename_columns(abcd_roi_sig)

# Load NDA information
nda_df = read_csv("../output/NDA_MID_QC_20230723.csv",show_col_types = F) %>% 
  select(subjectkey, interview_age, sex, site_id_l, scanner, p_puberty, y_puberty)
nda_df$subject = nda_df$subjectkey %>% gsub("_","",.)
nda_df$age = round(nda_df$interview_age/12,2)

# join datasets & remove those not needed
abcd_df = left_join(x = abcd_include_first, y = abcd_roi_sig, by = "subject") 
abcd_df = left_join(x = abcd_df, y = nda_df, by = "subject") %>% 
  select(-subjectkey,-subj)
abcd_df2 = left_join(x = abcd_include_second, y = abcd_roi_sig, by = "subject") 
abcd_df2 = left_join(x = abcd_df2, y = nda_df, by = "subject") %>% 
  select(-subjectkey,-subj)

# Round numeric values to 6th decimal to avoid positive definite errors
# Apply the function to all columns of the data frame
abcd_df[] <- lapply(abcd_df, round_var_3dec)
abcd_df2[] <- lapply(abcd_df2, round_var_3dec)


rm(abcd_id_include, nda_df, abcd_include_first,abcd_include_second, abcd_roi_sig,session_info)

2.2 AHRB

Load AHRB data

ahrb_id_include = read.csv("../output/AHRB/ahrb_final_subjs.tsv", sep = "\t", header = FALSE) 
colnames(ahrb_id_include) = c("subject")

ahrb_roi_sig = read.csv("../output/AHRB/region_roi-meansignal.csv", sep = ",", header = TRUE) %>% 
  rename(subject = "subj")
ahrb_roi_sig = rename_columns(ahrb_roi_sig)

# Load demo information
ahrb_dem = read_csv("../code_stage2/subject_details/AHRB_Participant_Details.csv",show_col_types = F) %>% 
  select(participant_id,age,sex) %>% 
  rename(subject="participant_id")


# join datasets & remove those not needed
ahrb_df = left_join(x = ahrb_id_include, y = ahrb_roi_sig, by = "subject")
ahrb_df = left_join(x = ahrb_df,y = ahrb_dem, by = "subject")
ahrb_df$subsample = "ahrb"

# round rois to 3 dec
ahrb_df[] <- lapply(ahrb_df, round_var_3dec)

rm(ahrb_id_include, ahrb_roi_sig, ahrb_dem)

2.3 MLS

Load MLS data

mls_id_include = read.csv("../output/MLS/mls_final_subjs.tsv", sep = "\t", header = FALSE) 
colnames(mls_id_include) = c("subject")

mls_roi_sig = read.csv("../output/mls/region_roi-meansignal.csv", sep = ",", header = TRUE) %>% 
  rename(subject = "subj")
mls_roi_sig = rename_columns(mls_roi_sig)

# Load demo information
mls_dem = read_tsv("../code_stage2/subject_details/MLS_Participant_Details.tsv",show_col_types = F) %>% 
  filter(StudyName==2) %>%
  arrange(participant_id) %>%
  group_by(participant_id) %>%
  mutate(session = paste0(row_number())) %>% 
  rename(subject="participant_id",age="ScanAge",sex="Sex") %>% 
  # Here we are filtering sess-1 labels the below IDs as their sess-2 scan is used per recommendation from MLS team (how they have worked with data historically)
  filter(!(subject %in% c("sub-05", "sub-106", "sub-11", "sub-118", "sub-123", "sub-210", 
                          "sub-24", "sub-27", "sub-29", "sub-44", "sub-54", "sub-64", 
                          "sub-88", "sub-92", "sub-97") & session == 1)) %>% 
  select(subject, age,sex) %>% 
  distinct(subject, .keep_all = TRUE)

# join datasets and remove those not needed
mls_df = left_join(x = mls_id_include, y = mls_roi_sig, by = "subject")
mls_df = left_join(x = mls_df, y = mls_dem, by = "subject")

mls_df$subsample = "mls"

#round to 6 dec
mls_df[] <- lapply(mls_df, round_var_3dec)

rm(mls_id_include, mls_roi_sig,mls_dem)

Relabel non-numerical variables, e.g., Sex and Race so it is interpreted as counts/% instead of means/sds

abcd_df$sex = if_else(abcd_df$sex=="M","Male","Female")
abcd_df2$sex = if_else(abcd_df2$sex=="M","Male","Female")
ahrb_df$sex = if_else(ahrb_df$sex==1,"Male","Female")
mls_df$sex = if_else(mls_df$sex==2,"Male","Female")

2.4 Combine Data

Specifying group sample labels (e.g., ABCD, AHRB, MLS). Then, combine the three datasets, abcd_df,ahrb_df & mls_df into single dataset using rbind() named brain_set. The set label is used as the group factoring in the cfa models.

# specific group set # and combined datasets using rbind
abcd_df$set = 'ABCD'
ahrb_df$set = 'AHRB'
mls_df$set = 'MLS'
abcd_df_r <- abcd_df[,c(1:50,52,57,58)]
brain_set = rbind(abcd_df_r,ahrb_df,mls_df)
rm(abcd_df_r)

2.5 Demographics of Samples

Report demographics (age/sex) across samples using the table1 for participants w/ available/usable ROI data.

Three tables:

1. table for the primary ABCD sample, the AHRB and MLS samples.
2. table for the held out ABCD sample

# Summary between releases
table1::label(brain_set$age) <- "Age (Years)"
table1::label(brain_set$sex) <- "Sex"


table1::table1(~age + sex | as.factor(set), data = brain_set)

	ABCD (N=346)	AHRB (N=97)	MLS (N=112)	Overall (N=555)
Age (Years)
Mean (SD)	12.0 (0.646)	19.3 (1.30)	20.2 (1.69)	15.0 (3.91)
Median [Min, Max]	12.0 [10.7, 13.5]	19.1 [17.0, 21.4]	20.2 [18.0, 26.0]	12.8 [10.7, 26.0]
Sex
Female	152 (43.9%)	56 (57.7%)	43 (38.4%)	251 (45.2%)
Male	194 (56.1%)	41 (42.3%)	69 (61.6%)	304 (54.8%)

# Summary between releases
table1::label(abcd_df2$age) <- "Age (Years)"
table1::label(abcd_df2$sex) <- "Sex"


table1::table1(~age + sex, data = abcd_df2)

	Overall (N=347)
Age (Years)
Mean (SD)	12.0 (0.678)
Median [Min, Max]	12.0 [10.8, 13.4]
Sex
Female	174 (50.1%)
Male	173 (49.9%)

3 ROIs Distribution/Correlations

Before running the models. Reviewing the distribution and properties of the ROI signals. To evaluate the bivariate point plots and distributions, the ggpairs() function is used. To display a bivariate correlation matrix for the a prior model regions of interest, both [cor()]https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/cor and corrplot() are used. For the 28 Nacc & Insula ROIs from the two runs across six contrast types, there are 378 unique correlations in the matrix. As stated in the registered report, the which() function is used identify any correlations that exceed r > |.85|. For the bivariate associations that exceed this a prior value the parameters will be fixed in the lavaan cfa models.

3.1 ABCD

3.1.1 Description of sites

combined_abcd_dfs = rbind(abcd_df[1:57],abcd_df2)
fir1k_plt <- abcd_df %>% 
  dplyr::group_by(site_id_l) %>% 
  dplyr::summarize(Sites = n()) %>%
  ungroup() %>% 
  ggplot(aes(x = site_id_l, y = Sites, fill = site_id_l)) +
  geom_text(aes(x = site_id_l, y = Sites, label = Sites), hjust = -.5) + # add text labels
  geom_bar(stat="identity", colour = "black", size = .1) +
  labs(title = "First 1000 samples across sites after exclusions",
       subtitle = "Initial per site n = 48") +
  xlab("Site Number") +
  ylab("Subj Count (n) per Site") +
  scale_fill_manual(values = pal) +
  coord_flip() +
  theme_minimal()

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

sec1k_plt <- abcd_df2 %>% 
  dplyr::group_by(site_id_l) %>% 
  dplyr::summarize(Sites = n()) %>%
  ungroup() %>% 
  ggplot(aes(x = site_id_l, y = Sites, fill = site_id_l)) +
  geom_bar(stat="identity", colour = "black", size = .1) +
  geom_text(aes(x = site_id_l, y = Sites, label = Sites), hjust = -.5) + # add text labels
  labs(title = "Second 1000 samples across sites after exclusions",
       subtitle = "Initial per site n = 48") +
  xlab("Site Number") +
  ylab("Subj Count (n) per Site") +
  scale_fill_manual(values = pal) +
  coord_flip() +
  theme_minimal()

comb2k_plt <- combined_abcd_dfs %>% 
  dplyr::group_by(site_id_l) %>% 
  dplyr::summarize(Sites = n()) %>%
  ungroup() %>% 
  ggplot(aes(x = site_id_l, y = Sites, fill = site_id_l)) +
  geom_bar(stat="identity", colour = "black", size = .1) +
  geom_text(aes(x = site_id_l, y = Sites, label = Sites), hjust = -.5) + # add text labels
  labs(title = "Combined 2000 samples across sites after exclusions",
       subtitle = "Initial per site n = 96") +
  xlab("Site Number") +
  ylab("Subj Count (n) per Site") +
  scale_fill_manual(values = pal) +
  coord_flip() +
  theme_minimal()

combscan_plt <- combined_abcd_dfs %>% 
  dplyr::group_by(scanner) %>% 
  dplyr::summarize(scan_n = n()) %>%
  ungroup() %>% 
  ggplot(aes(x = scanner, y = scan_n, fill = scanner)) +
  geom_bar(stat="identity", colour = "black", size = .1) +
  geom_text(aes(x = scanner, y = scan_n, label = scan_n), hjust = -0.5) + # add text labels
  labs(title = "Combined 2000 samples across scanners after exclusions",
       subtitle = "Initial: 1245 SIEMENS, 257 Philips, 479 GE") +
  xlab("Site Number") +
  ylab("Subj Count (n) per Site") +
  ylim(c(0,800))+
  scale_fill_manual(values = pal) +
  coord_flip() +
  theme_minimal()

fir1k_plt

sec1k_plt

comb2k_plt

combscan_plt

3.1.2 Export IDs

Export subject IDs for each site and scanner to use in group [cohen’s D] contrast maps

3.1.3 Correlations

Plot correlation matrix only of Left/Right NAcc and Insula mean signal intensity values for Contrasts and Regions used in the MID population model. (Note: diagonal is set to 0)

abcd_cor = cor(abcd_df[,mod_vars]) 

# numeric+string style names for correlation table 
numstr_row <- row.names(abcd_cor)
numstr_modrow_names <- paste0(1:28, "_", numstr_row)
numstr_col <- colnames(abcd_cor)
numstr_modcol_names <- paste0(1:28, "_", numstr_col)

# Create table
row.names(abcd_cor) <- numstr_modrow_names
colnames(abcd_cor) <- numstr_modcol_names
kable(as.data.frame(abcd_cor), booktabs = TRUE) %>%
  kable_styling(font_size = 8,position = 'center')

	1_AWin_v_Neut_L_NAc_r1	2_AWin_v_Neut_R_NAc_r1	3_AWin_v_Neut_L_NAc_r2	4_AWin_v_Neut_R_NAc_r2	5_BWin_v_Neut_L_NAc_r1	6_BWin_v_Neut_R_NAc_r1	7_BWin_v_Neut_L_NAc_r2	8_BWin_v_Neut_R_NAc_r2	9_BWin_v_BLose_L_NAc_r1	10_BWin_v_BLose_R_NAc_r1	11_BWin_v_BLose_L_NAc_r2	12_BWin_v_BLose_R_NAc_r2	13_AWin_v_Neut_R_Ins_r1	14_AWin_v_Neut_R_Ins_r2	15_BWin_v_Neut_R_Ins_r1	16_BWin_v_Neut_R_Ins_r2	17_ALose_v_Neut_L_Ins_r1	18_ALose_v_Neut_R_Ins_r1	19_ALose_v_Neut_L_Ins_r2	20_ALose_v_Neut_R_Ins_r2	21_BLose_v_Neut_L_Ins_r1	22_BLose_v_Neut_R_Ins_r1	23_BLose_v_Neut_L_Ins_r2	24_BLose_v_Neut_R_Ins_r2	25_BLose_v_BWin_L_Ins_r1	26_BLose_v_BWin_R_Ins_r1	27_BLose_v_BWin_L_Ins_r2	28_BLose_v_BWin_R_Ins_r2
1_AWin_v_Neut_L_NAc_r1	1.0000000	0.5950797	0.2139166	0.1465296	0.8845134	0.5330021	0.2001355	0.1435928	0.3354544	0.2597103	0.0339825	0.0115115	0.1851053	0.0199938	0.1746626	0.0477703	0.1640808	0.1153632	0.0981073	0.0346380	0.2004769	0.1268074	0.0573609	0.0078758	-0.0821144	-0.0647178	-0.0192609	-0.0385100
2_AWin_v_Neut_R_NAc_r1	0.5950797	1.0000000	0.2038607	0.1636949	0.5536385	0.8937679	0.1817447	0.1496599	0.2554489	0.4330457	-0.0191448	-0.0458138	0.1484618	-0.0044368	0.1617020	-0.0207709	0.1366151	0.0985286	0.0372230	-0.0161941	0.1268962	0.0741686	0.0098690	-0.0407126	-0.1266538	-0.0981254	0.0479248	-0.0240983
3_AWin_v_Neut_L_NAc_r2	0.2139166	0.2038607	1.0000000	0.6579877	0.2584135	0.2502372	0.8959386	0.5663426	0.1590999	0.1698065	0.3206650	0.2306648	-0.0580876	0.2379255	-0.0337876	0.1734178	-0.0051049	-0.0900681	0.1102763	0.0989235	-0.0070956	-0.0804845	0.1024636	0.0504413	-0.0137024	-0.0369702	-0.1328174	-0.1156633
4_AWin_v_Neut_R_NAc_r2	0.1465296	0.1636949	0.6579877	1.0000000	0.1674712	0.1725353	0.5985384	0.8931364	0.1471856	0.1171676	0.1936098	0.3385741	-0.0641605	0.2569921	-0.0302412	0.2311233	-0.0165031	-0.0942152	0.1303503	0.1647277	-0.0229582	-0.1006499	0.1703589	0.1470004	-0.0438219	-0.0584066	-0.0334909	-0.0670002
5_BWin_v_Neut_L_NAc_r1	0.8845134	0.5536385	0.2584135	0.1674712	1.0000000	0.6250684	0.2579271	0.1702415	0.5247650	0.3805786	0.0764875	0.0385365	0.1799387	0.0224945	0.2211758	0.0464932	0.1190014	0.0634082	0.1259629	0.0412504	0.1528295	0.0804730	0.0878025	0.0221013	-0.1580731	-0.1525971	0.0093442	-0.0216219
6_BWin_v_Neut_R_NAc_r1	0.5330021	0.8937679	0.2502372	0.1725353	0.6250684	1.0000000	0.2388305	0.1698549	0.3485564	0.5794210	-0.0019084	-0.0357901	0.1556295	0.0309308	0.2107298	0.0149424	0.1175050	0.0590179	0.0521981	0.0111445	0.1203580	0.0432876	0.0299376	-0.0043651	-0.1670254	-0.1748785	0.0465895	-0.0194930
7_BWin_v_Neut_L_NAc_r2	0.2001355	0.1817447	0.8959386	0.5985384	0.2579271	0.2388305	1.0000000	0.6380893	0.1872819	0.1896098	0.4830477	0.3309468	-0.0616141	0.1890490	-0.0168875	0.1978692	-0.0522485	-0.1235289	0.0921457	0.0822917	-0.0424914	-0.0918091	0.0705100	0.0496501	-0.0689890	-0.0640682	-0.2208008	-0.1407310
8_BWin_v_Neut_R_NAc_r2	0.1435928	0.1496599	0.5663426	0.8931364	0.1702415	0.1698549	0.6380893	1.0000000	0.1597151	0.1439030	0.2979038	0.5094028	-0.0929192	0.1773221	-0.0527010	0.2135452	-0.0529229	-0.1336891	0.0966856	0.0870560	-0.0454363	-0.1215713	0.1295632	0.0956410	-0.0664160	-0.0541640	-0.1174692	-0.1059791
9_BWin_v_BLose_L_NAc_r1	0.3354544	0.2554489	0.1590999	0.1471856	0.5247650	0.3485564	0.1872819	0.1597151	1.0000000	0.6191471	0.0859933	0.0417368	0.1419665	0.0054686	0.2097957	0.0252722	-0.1020563	-0.1186395	0.0608246	0.0298211	-0.1084084	-0.1559031	0.0749824	0.0417623	-0.3477992	-0.3497189	0.0651652	0.0206209
10_BWin_v_BLose_R_NAc_r1	0.2597103	0.4330457	0.1698065	0.1171676	0.3805786	0.5794210	0.1896098	0.1439030	0.6191471	1.0000000	0.0743800	0.0147475	0.1278645	-0.0112828	0.1996461	-0.0085837	0.0171696	-0.0590937	-0.0007143	0.0046034	-0.0054182	-0.0935556	0.0052799	0.0144032	-0.2849182	-0.2845167	0.0666777	0.0241004
11_BWin_v_BLose_L_NAc_r2	0.0339825	-0.0191448	0.3206650	0.1936098	0.0764875	-0.0019084	0.4830477	0.2979038	0.0859933	0.0743800	1.0000000	0.6010950	-0.1097000	-0.0566479	-0.1213601	0.0127401	-0.1129387	-0.1366714	-0.1218098	-0.1805984	-0.1067887	-0.0797302	-0.1815603	-0.2006821	-0.0227356	0.0522930	-0.3104904	-0.2326244
12_BWin_v_BLose_R_NAc_r2	0.0115115	-0.0458138	0.2306648	0.3385741	0.0385365	-0.0357901	0.3309468	0.5094028	0.0417368	0.0147475	0.6010950	1.0000000	-0.1716879	-0.0715049	-0.1574185	-0.0017498	-0.1060272	-0.1854076	-0.1603961	-0.2107428	-0.1057521	-0.1371138	-0.2003796	-0.2248105	-0.0066444	0.0379775	-0.2930188	-0.2448287
13_AWin_v_Neut_R_Ins_r1	0.1851053	0.1484618	-0.0580876	-0.0641605	0.1799387	0.1556295	-0.0616141	-0.0929192	0.1419665	0.1278645	-0.1097000	-0.1716879	1.0000000	0.0848943	0.8793139	0.0222896	0.4140705	0.6174249	0.1832810	0.1350309	0.3822399	0.5054902	0.1849825	0.1349478	-0.2508752	-0.4426264	0.1267355	0.1258750
14_AWin_v_Neut_R_Ins_r2	0.0199938	-0.0044368	0.2379255	0.2569921	0.0224945	0.0309308	0.1890490	0.1773221	0.0054686	-0.0112828	-0.0566479	-0.0715049	0.0848943	1.0000000	0.1156336	0.8702560	0.1008386	0.1057984	0.4196794	0.6807837	0.0946191	0.1085440	0.4044773	0.5671231	0.0003008	-0.0210608	-0.1152049	-0.2370428
15_BWin_v_Neut_R_Ins_r1	0.1746626	0.1617020	-0.0337876	-0.0302412	0.2211758	0.2107298	-0.0168875	-0.0527010	0.2097957	0.1996461	-0.1213601	-0.1574185	0.8793139	0.1156336	1.0000000	0.0438838	0.3976692	0.5542318	0.1909067	0.1630639	0.3577843	0.4490304	0.1937409	0.1594272	-0.3665808	-0.6144718	0.1201384	0.1312946
16_BWin_v_Neut_R_Ins_r2	0.0477703	-0.0207709	0.1734178	0.2311233	0.0464932	0.0149424	0.1978692	0.2135452	0.0252722	-0.0085837	0.0127401	-0.0017498	0.0222896	0.8702560	0.0438838	1.0000000	0.0327644	0.0421346	0.3882707	0.6349284	0.0338597	0.0551187	0.3755355	0.5432330	0.0261708	0.0043050	-0.2427214	-0.3912590
17_ALose_v_Neut_L_Ins_r1	0.1640808	0.1366151	-0.0051049	-0.0165031	0.1190014	0.1175050	-0.0522485	-0.0529229	-0.1020563	0.0171696	-0.1129387	-0.1060272	0.4140705	0.1008386	0.3976692	0.0327644	1.0000000	0.6182345	0.1306261	0.0871469	0.8928451	0.5424748	0.0868636	0.0332482	0.2405338	0.0770004	0.0016191	0.0043210
18_ALose_v_Neut_R_Ins_r1	0.1153632	0.0985286	-0.0900681	-0.0942152	0.0634082	0.0590179	-0.1235289	-0.1336891	-0.1186395	-0.0590937	-0.1366714	-0.1854076	0.6174249	0.1057984	0.5542318	0.0421346	0.6182345	1.0000000	0.1585425	0.1152819	0.5509158	0.8553356	0.1649781	0.1003633	0.2016749	0.1949284	0.0822512	0.0685096
19_ALose_v_Neut_L_Ins_r2	0.0981073	0.0372230	0.1102763	0.1303503	0.1259629	0.0521981	0.0921457	0.0966856	0.0608246	-0.0007143	-0.1218098	-0.1603961	0.1832810	0.4196794	0.1909067	0.3882707	0.1306261	0.1585425	1.0000000	0.7076302	0.1205029	0.1176091	0.8631333	0.6109065	-0.0878578	-0.0891215	0.3430005	0.2866485
20_ALose_v_Neut_R_Ins_r2	0.0346380	-0.0161941	0.0989235	0.1647277	0.0412504	0.0111445	0.0822917	0.0870560	0.0298211	0.0046034	-0.1805984	-0.2107428	0.1350309	0.6807837	0.1630639	0.6349284	0.0871469	0.1152819	0.7076302	1.0000000	0.1124738	0.1265568	0.6471309	0.8762268	-0.0493096	-0.0531370	0.2692215	0.3339270
21_BLose_v_Neut_L_Ins_r1	0.2004769	0.1268962	-0.0070956	-0.0229582	0.1528295	0.1203580	-0.0424914	-0.0454363	-0.1084084	-0.0054182	-0.1067887	-0.1057521	0.3822399	0.0946191	0.3577843	0.0338597	0.8928451	0.5509158	0.1205029	0.1124738	1.0000000	0.6317566	0.0661950	0.0622222	0.4130309	0.1960989	-0.0040007	0.0349029
22_BLose_v_Neut_R_Ins_r1	0.1268074	0.0741686	-0.0804845	-0.1006499	0.0804730	0.0432876	-0.0918091	-0.1215713	-0.1559031	-0.0935556	-0.0797302	-0.1371138	0.5054902	0.1085440	0.4490304	0.0551187	0.5424748	0.8553356	0.1176091	0.1265568	0.6317566	1.0000000	0.1142027	0.1161500	0.3367126	0.4290105	0.0333868	0.0730219
23_BLose_v_Neut_L_Ins_r2	0.0573609	0.0098690	0.1024636	0.1703589	0.0878025	0.0299376	0.0705100	0.1295632	0.0749824	0.0052799	-0.1815603	-0.2003796	0.1849825	0.4044773	0.1937409	0.3755355	0.0868636	0.1649781	0.8631333	0.6471309	0.0661950	0.1142027	1.0000000	0.7274828	-0.1213241	-0.0950665	0.5184734	0.4270089
24_BLose_v_Neut_R_Ins_r2	0.0078758	-0.0407126	0.0504413	0.1470004	0.0221013	-0.0043651	0.0496501	0.0956410	0.0417623	0.0144032	-0.2006821	-0.2248105	0.1349478	0.5671231	0.1594272	0.5432330	0.0332482	0.1003633	0.6109065	0.8762268	0.0622222	0.1161500	0.7274828	1.0000000	-0.0555129	-0.0587289	0.3754039	0.5601036
25_BLose_v_BWin_L_Ins_r1	-0.0821144	-0.1266538	-0.0137024	-0.0438219	-0.1580731	-0.1670254	-0.0689890	-0.0664160	-0.3477992	-0.2849182	-0.0227356	-0.0066444	-0.2508752	0.0003008	-0.3665808	0.0261708	0.2405338	0.2016749	-0.0878578	-0.0493096	0.4130309	0.3367126	-0.1213241	-0.0555129	1.0000000	0.6679275	-0.1067048	-0.0866290
26_BLose_v_BWin_R_Ins_r1	-0.0647178	-0.0981254	-0.0369702	-0.0584066	-0.1525971	-0.1748785	-0.0640682	-0.0541640	-0.3497189	-0.2845167	0.0522930	0.0379775	-0.4426264	-0.0210608	-0.6144718	0.0043050	0.0770004	0.1949284	-0.0891215	-0.0531370	0.1960989	0.4290105	-0.0950665	-0.0587289	0.6679275	1.0000000	-0.0921072	-0.0683809
27_BLose_v_BWin_L_Ins_r2	-0.0192609	0.0479248	-0.1328174	-0.0334909	0.0093442	0.0465895	-0.2208008	-0.1174692	0.0651652	0.0666777	-0.3104904	-0.2930188	0.1267355	-0.1152049	0.1201384	-0.2427214	0.0016191	0.0822512	0.3430005	0.2692215	-0.0040007	0.0333868	0.5184734	0.3754039	-0.1067048	-0.0921072	1.0000000	0.6510396
28_BLose_v_BWin_R_Ins_r2	-0.0385100	-0.0240983	-0.1156633	-0.0670002	-0.0216219	-0.0194930	-0.1407310	-0.1059791	0.0206209	0.0241004	-0.2326244	-0.2448287	0.1258750	-0.2370428	0.1312946	-0.3912590	0.0043210	0.0685096	0.2866485	0.3339270	0.0349029	0.0730219	0.4270089	0.5601036	-0.0866290	-0.0683809	0.6510396	1.0000000

# Numeric only for plot
numeric_row <- paste0(1:nrow(abcd_cor))
numeric_col <- paste0(1:nrow(abcd_cor))
rownames(abcd_cor) <- numeric_row
colnames(abcd_cor) <- numeric_col

a_cor_plt <- corrplot(abcd_cor , method = "color", tl.cex = .6, diag = TRUE)

a_cor_plt

## $corr
##               1            2            3           4            5            6
## 1   1.000000000  0.595079719  0.213916568  0.14652961  0.884513447  0.533002084
## 2   0.595079719  1.000000000  0.203860691  0.16369491  0.553638472  0.893767862
## 3   0.213916568  0.203860691  1.000000000  0.65798773  0.258413492  0.250237163
## 4   0.146529609  0.163694914  0.657987730  1.00000000  0.167471159  0.172535317
## 5   0.884513447  0.553638472  0.258413492  0.16747116  1.000000000  0.625068420
## 6   0.533002084  0.893767862  0.250237163  0.17253532  0.625068420  1.000000000
## 7   0.200135497  0.181744740  0.895938617  0.59853837  0.257927108  0.238830475
## 8   0.143592816  0.149659921  0.566342615  0.89313636  0.170241525  0.169854929
## 9   0.335454352  0.255448879  0.159099864  0.14718561  0.524765000  0.348556408
## 10  0.259710336  0.433045719  0.169806514  0.11716756  0.380578560  0.579421050
## 11  0.033982546 -0.019144834  0.320665049  0.19360977  0.076487472 -0.001908373
## 12  0.011511537 -0.045813793  0.230664772  0.33857406  0.038536515 -0.035790086
## 13  0.185105279  0.148461771 -0.058087612 -0.06416051  0.179938722  0.155629506
## 14  0.019993769 -0.004436825  0.237925549  0.25699213  0.022494532  0.030930783
## 15  0.174662600  0.161701994 -0.033787589 -0.03024121  0.221175819  0.210729826
## 16  0.047770310 -0.020770890  0.173417777  0.23112328  0.046493169  0.014942415
## 17  0.164080816  0.136615076 -0.005104915 -0.01650310  0.119001395  0.117505036
## 18  0.115363157  0.098528648 -0.090068115 -0.09421517  0.063408224  0.059017932
## 19  0.098107323  0.037223029  0.110276343  0.13035027  0.125962896  0.052198081
## 20  0.034638033 -0.016194066  0.098923549  0.16472773  0.041250383  0.011144482
## 21  0.200476930  0.126896222 -0.007095617 -0.02295825  0.152829506  0.120357970
## 22  0.126807420  0.074168614 -0.080484465 -0.10064988  0.080472990  0.043287576
## 23  0.057360928  0.009869006  0.102463573  0.17035894  0.087802455  0.029937576
## 24  0.007875783 -0.040712607  0.050441332  0.14700044  0.022101312 -0.004365119
## 25 -0.082114375 -0.126653815 -0.013702367 -0.04382186 -0.158073075 -0.167025437
## 26 -0.064717827 -0.098125422 -0.036970179 -0.05840664 -0.152597088 -0.174878531
## 27 -0.019260853  0.047924847 -0.132817393 -0.03349087  0.009344218  0.046589520
## 28 -0.038509964 -0.024098268 -0.115663289 -0.06700021 -0.021621948 -0.019492971
##              7           8            9            10           11           12
## 1   0.20013550  0.14359282  0.335454352  0.2597103357  0.033982546  0.011511537
## 2   0.18174474  0.14965992  0.255448879  0.4330457188 -0.019144834 -0.045813793
## 3   0.89593862  0.56634262  0.159099864  0.1698065141  0.320665049  0.230664772
## 4   0.59853837  0.89313636  0.147185612  0.1171675558  0.193609774  0.338574062
## 5   0.25792711  0.17024152  0.524765000  0.3805785595  0.076487472  0.038536515
## 6   0.23883047  0.16985493  0.348556408  0.5794210496 -0.001908373 -0.035790086
## 7   1.00000000  0.63808926  0.187281939  0.1896097700  0.483047720  0.330946837
## 8   0.63808926  1.00000000  0.159715093  0.1439030047  0.297903765  0.509402793
## 9   0.18728194  0.15971509  1.000000000  0.6191470969  0.085993285  0.041736765
## 10  0.18960977  0.14390300  0.619147097  1.0000000000  0.074379965  0.014747450
## 11  0.48304772  0.29790377  0.085993285  0.0743799653  1.000000000  0.601095020
## 12  0.33094684  0.50940279  0.041736765  0.0147474504  0.601095020  1.000000000
## 13 -0.06161412 -0.09291925  0.141966483  0.1278645398 -0.109699998 -0.171687863
## 14  0.18904900  0.17732206  0.005468646 -0.0112827652 -0.056647893 -0.071504883
## 15 -0.01688753 -0.05270098  0.209795700  0.1996461297 -0.121360121 -0.157418484
## 16  0.19786921  0.21354525  0.025272196 -0.0085837441  0.012740094 -0.001749762
## 17 -0.05224854 -0.05292286 -0.102056255  0.0171695789 -0.112938677 -0.106027201
## 18 -0.12352885 -0.13368908 -0.118639510 -0.0590937213 -0.136671365 -0.185407565
## 19  0.09214569  0.09668556  0.060824644 -0.0007143294 -0.121809777 -0.160396147
## 20  0.08229167  0.08705605  0.029821075  0.0046034169 -0.180598402 -0.210742779
## 21 -0.04249143 -0.04543626 -0.108408389 -0.0054182146 -0.106788673 -0.105752058
## 22 -0.09180911 -0.12157128 -0.155903070 -0.0935556206 -0.079730220 -0.137113780
## 23  0.07051003  0.12956321  0.074982357  0.0052799040 -0.181560280 -0.200379590
## 24  0.04965014  0.09564100  0.041762274  0.0144032307 -0.200682065 -0.224810534
## 25 -0.06898898 -0.06641598 -0.347799206 -0.2849182341 -0.022735605 -0.006644424
## 26 -0.06406825 -0.05416397 -0.349718867 -0.2845167070  0.052293023  0.037977485
## 27 -0.22080084 -0.11746917  0.065165218  0.0666776581 -0.310490389 -0.293018774
## 28 -0.14073103 -0.10597909  0.020620925  0.0241004025 -0.232624405 -0.244828692
##             13           14          15           16           17          18
## 1   0.18510528  0.019993769  0.17466260  0.047770310  0.164080816  0.11536316
## 2   0.14846177 -0.004436825  0.16170199 -0.020770890  0.136615076  0.09852865
## 3  -0.05808761  0.237925549 -0.03378759  0.173417777 -0.005104915 -0.09006811
## 4  -0.06416051  0.256992130 -0.03024121  0.231123277 -0.016503104 -0.09421517
## 5   0.17993872  0.022494532  0.22117582  0.046493169  0.119001395  0.06340822
## 6   0.15562951  0.030930783  0.21072983  0.014942415  0.117505036  0.05901793
## 7  -0.06161412  0.189048999 -0.01688753  0.197869205 -0.052248541 -0.12352885
## 8  -0.09291925  0.177322059 -0.05270098  0.213545247 -0.052922860 -0.13368908
## 9   0.14196648  0.005468646  0.20979570  0.025272196 -0.102056255 -0.11863951
## 10  0.12786454 -0.011282765  0.19964613 -0.008583744  0.017169579 -0.05909372
## 11 -0.10970000 -0.056647893 -0.12136012  0.012740094 -0.112938677 -0.13667136
## 12 -0.17168786 -0.071504883 -0.15741848 -0.001749762 -0.106027201 -0.18540756
## 13  1.00000000  0.084894341  0.87931388  0.022289568  0.414070548  0.61742491
## 14  0.08489434  1.000000000  0.11563357  0.870255990  0.100838627  0.10579843
## 15  0.87931388  0.115633574  1.00000000  0.043883786  0.397669156  0.55423179
## 16  0.02228957  0.870255990  0.04388379  1.000000000  0.032764413  0.04213459
## 17  0.41407055  0.100838627  0.39766916  0.032764413  1.000000000  0.61823453
## 18  0.61742491  0.105798433  0.55423179  0.042134590  0.618234528  1.00000000
## 19  0.18328103  0.419679366  0.19090665  0.388270699  0.130626089  0.15854249
## 20  0.13503087  0.680783653  0.16306392  0.634928428  0.087146863  0.11528187
## 21  0.38223993  0.094619090  0.35778428  0.033859716  0.892845071  0.55091579
## 22  0.50549023  0.108544018  0.44903037  0.055118689  0.542474817  0.85533558
## 23  0.18498255  0.404477312  0.19374087  0.375535465  0.086863642  0.16497812
## 24  0.13494782  0.567123084  0.15942722  0.543232987  0.033248178  0.10036328
## 25 -0.25087518  0.000300767 -0.36658077  0.026170788  0.240533821  0.20167491
## 26 -0.44262637 -0.021060835 -0.61447180  0.004304981  0.077000384  0.19492844
## 27  0.12673553 -0.115204930  0.12013836 -0.242721401  0.001619121  0.08225119
## 28  0.12587498 -0.237042817  0.13129460 -0.391259017  0.004321026  0.06850961
##               19           20           21          22           23
## 1   0.0981073231  0.034638033  0.200476930  0.12680742  0.057360928
## 2   0.0372230287 -0.016194066  0.126896222  0.07416861  0.009869006
## 3   0.1102763434  0.098923549 -0.007095617 -0.08048446  0.102463573
## 4   0.1303502685  0.164727727 -0.022958249 -0.10064988  0.170358938
## 5   0.1259628957  0.041250383  0.152829506  0.08047299  0.087802455
## 6   0.0521980812  0.011144482  0.120357970  0.04328758  0.029937576
## 7   0.0921456874  0.082291672 -0.042491432 -0.09180911  0.070510034
## 8   0.0966855638  0.087056046 -0.045436259 -0.12157128  0.129563209
## 9   0.0608246439  0.029821075 -0.108408389 -0.15590307  0.074982357
## 10 -0.0007143294  0.004603417 -0.005418215 -0.09355562  0.005279904
## 11 -0.1218097766 -0.180598402 -0.106788673 -0.07973022 -0.181560280
## 12 -0.1603961469 -0.210742779 -0.105752058 -0.13711378 -0.200379590
## 13  0.1832810251  0.135030872  0.382239933  0.50549023  0.184982545
## 14  0.4196793658  0.680783653  0.094619090  0.10854402  0.404477312
## 15  0.1909066525  0.163063917  0.357784280  0.44903037  0.193740870
## 16  0.3882706994  0.634928428  0.033859716  0.05511869  0.375535465
## 17  0.1306260892  0.087146863  0.892845071  0.54247482  0.086863642
## 18  0.1585424852  0.115281873  0.550915789  0.85533558  0.164978117
## 19  1.0000000000  0.707630203  0.120502925  0.11760909  0.863133299
## 20  0.7076302034  1.000000000  0.112473770  0.12655683  0.647130906
## 21  0.1205029250  0.112473770  1.000000000  0.63175656  0.066195024
## 22  0.1176090896  0.126556831  0.631756555  1.00000000  0.114202689
## 23  0.8631332985  0.647130906  0.066195024  0.11420269  1.000000000
## 24  0.6109065361  0.876226825  0.062222243  0.11615003  0.727482813
## 25 -0.0878578147 -0.049309615  0.413030935  0.33671256 -0.121324146
## 26 -0.0891214805 -0.053137030  0.196098858  0.42901046 -0.095066492
## 27  0.3430005340  0.269221511 -0.004000714  0.03338681  0.518473405
## 28  0.2866485245  0.333926984  0.034902940  0.07302190  0.427008941
##              24           25           26           27           28
## 1   0.007875783 -0.082114375 -0.064717827 -0.019260853 -0.038509964
## 2  -0.040712607 -0.126653815 -0.098125422  0.047924847 -0.024098268
## 3   0.050441332 -0.013702367 -0.036970179 -0.132817393 -0.115663289
## 4   0.147000436 -0.043821859 -0.058406635 -0.033490873 -0.067000210
## 5   0.022101312 -0.158073075 -0.152597088  0.009344218 -0.021621948
## 6  -0.004365119 -0.167025437 -0.174878531  0.046589520 -0.019492971
## 7   0.049650138 -0.068988983 -0.064068249 -0.220800837 -0.140731032
## 8   0.095640996 -0.066415978 -0.054163970 -0.117469169 -0.105979090
## 9   0.041762274 -0.347799206 -0.349718867  0.065165218  0.020620925
## 10  0.014403231 -0.284918234 -0.284516707  0.066677658  0.024100403
## 11 -0.200682065 -0.022735605  0.052293023 -0.310490389 -0.232624405
## 12 -0.224810534 -0.006644424  0.037977485 -0.293018774 -0.244828692
## 13  0.134947818 -0.250875179 -0.442626366  0.126735527  0.125874981
## 14  0.567123084  0.000300767 -0.021060835 -0.115204930 -0.237042817
## 15  0.159427220 -0.366580772 -0.614471804  0.120138356  0.131294601
## 16  0.543232987  0.026170788  0.004304981 -0.242721401 -0.391259017
## 17  0.033248178  0.240533821  0.077000384  0.001619121  0.004321026
## 18  0.100363280  0.201674910  0.194928441  0.082251191  0.068509614
## 19  0.610906536 -0.087857815 -0.089121481  0.343000534  0.286648525
## 20  0.876226825 -0.049309615 -0.053137030  0.269221511  0.333926984
## 21  0.062222243  0.413030935  0.196098858 -0.004000714  0.034902940
## 22  0.116150032  0.336712561  0.429010455  0.033386812  0.073021903
## 23  0.727482813 -0.121324146 -0.095066492  0.518473405  0.427008941
## 24  1.000000000 -0.055512893 -0.058728927  0.375403900  0.560103554
## 25 -0.055512893  1.000000000  0.667927470 -0.106704781 -0.086628982
## 26 -0.058728927  0.667927470  1.000000000 -0.092107177 -0.068380934
## 27  0.375403900 -0.106704781 -0.092107177  1.000000000  0.651039597
## 28  0.560103554 -0.086628982 -0.068380934  0.651039597  1.000000000
## 
## $corrPos
##     xName yName  x  y          corr
## 1       1     1  1 28  1.0000000000
## 2       1     2  1 27  0.5950797193
## 3       1     3  1 26  0.2139165676
## 4       1     4  1 25  0.1465296091
## 5       1     5  1 24  0.8845134474
## 6       1     6  1 23  0.5330020838
## 7       1     7  1 22  0.2001354972
## 8       1     8  1 21  0.1435928158
## 9       1     9  1 20  0.3354543521
## 10      1    10  1 19  0.2597103357
## 11      1    11  1 18  0.0339825465
## 12      1    12  1 17  0.0115115369
## 13      1    13  1 16  0.1851052787
## 14      1    14  1 15  0.0199937691
## 15      1    15  1 14  0.1746626000
## 16      1    16  1 13  0.0477703097
## 17      1    17  1 12  0.1640808158
## 18      1    18  1 11  0.1153631567
## 19      1    19  1 10  0.0981073231
## 20      1    20  1  9  0.0346380332
## 21      1    21  1  8  0.2004769304
## 22      1    22  1  7  0.1268074199
## 23      1    23  1  6  0.0573609285
## 24      1    24  1  5  0.0078757829
## 25      1    25  1  4 -0.0821143751
## 26      1    26  1  3 -0.0647178269
## 27      1    27  1  2 -0.0192608529
## 28      1    28  1  1 -0.0385099639
## 29      2     1  2 28  0.5950797193
## 30      2     2  2 27  1.0000000000
## 31      2     3  2 26  0.2038606912
## 32      2     4  2 25  0.1636949142
## 33      2     5  2 24  0.5536384721
## 34      2     6  2 23  0.8937678624
## 35      2     7  2 22  0.1817447400
## 36      2     8  2 21  0.1496599211
## 37      2     9  2 20  0.2554488792
## 38      2    10  2 19  0.4330457188
## 39      2    11  2 18 -0.0191448341
## 40      2    12  2 17 -0.0458137926
## 41      2    13  2 16  0.1484617714
## 42      2    14  2 15 -0.0044368247
## 43      2    15  2 14  0.1617019942
## 44      2    16  2 13 -0.0207708897
## 45      2    17  2 12  0.1366150760
## 46      2    18  2 11  0.0985286478
## 47      2    19  2 10  0.0372230287
## 48      2    20  2  9 -0.0161940661
## 49      2    21  2  8  0.1268962223
## 50      2    22  2  7  0.0741686136
## 51      2    23  2  6  0.0098690056
## 52      2    24  2  5 -0.0407126065
## 53      2    25  2  4 -0.1266538151
## 54      2    26  2  3 -0.0981254222
## 55      2    27  2  2  0.0479248469
## 56      2    28  2  1 -0.0240982679
## 57      3     1  3 28  0.2139165676
## 58      3     2  3 27  0.2038606912
## 59      3     3  3 26  1.0000000000
## 60      3     4  3 25  0.6579877303
## 61      3     5  3 24  0.2584134918
## 62      3     6  3 23  0.2502371633
## 63      3     7  3 22  0.8959386168
## 64      3     8  3 21  0.5663426153
## 65      3     9  3 20  0.1590998642
## 66      3    10  3 19  0.1698065141
## 67      3    11  3 18  0.3206650488
## 68      3    12  3 17  0.2306647722
## 69      3    13  3 16 -0.0580876115
## 70      3    14  3 15  0.2379255490
## 71      3    15  3 14 -0.0337875894
## 72      3    16  3 13  0.1734177768
## 73      3    17  3 12 -0.0051049154
## 74      3    18  3 11 -0.0900681149
## 75      3    19  3 10  0.1102763434
## 76      3    20  3  9  0.0989235486
## 77      3    21  3  8 -0.0070956174
## 78      3    22  3  7 -0.0804844646
## 79      3    23  3  6  0.1024635727
## 80      3    24  3  5  0.0504413323
## 81      3    25  3  4 -0.0137023668
## 82      3    26  3  3 -0.0369701789
## 83      3    27  3  2 -0.1328173925
## 84      3    28  3  1 -0.1156632887
## 85      4     1  4 28  0.1465296091
## 86      4     2  4 27  0.1636949142
## 87      4     3  4 26  0.6579877303
## 88      4     4  4 25  1.0000000000
## 89      4     5  4 24  0.1674711592
## 90      4     6  4 23  0.1725353173
## 91      4     7  4 22  0.5985383711
## 92      4     8  4 21  0.8931363557
## 93      4     9  4 20  0.1471856123
## 94      4    10  4 19  0.1171675558
## 95      4    11  4 18  0.1936097739
## 96      4    12  4 17  0.3385740616
## 97      4    13  4 16 -0.0641605109
## 98      4    14  4 15  0.2569921303
## 99      4    15  4 14 -0.0302412060
## 100     4    16  4 13  0.2311232770
## 101     4    17  4 12 -0.0165031044
## 102     4    18  4 11 -0.0942151651
## 103     4    19  4 10  0.1303502685
## 104     4    20  4  9  0.1647277269
## 105     4    21  4  8 -0.0229582490
## 106     4    22  4  7 -0.1006498834
## 107     4    23  4  6  0.1703589375
## 108     4    24  4  5  0.1470004360
## 109     4    25  4  4 -0.0438218586
## 110     4    26  4  3 -0.0584066354
## 111     4    27  4  2 -0.0334908731
## 112     4    28  4  1 -0.0670002102
## 113     5     1  5 28  0.8845134474
## 114     5     2  5 27  0.5536384721
## 115     5     3  5 26  0.2584134918
## 116     5     4  5 25  0.1674711592
## 117     5     5  5 24  1.0000000000
## 118     5     6  5 23  0.6250684205
## 119     5     7  5 22  0.2579271084
## 120     5     8  5 21  0.1702415247
## 121     5     9  5 20  0.5247650003
## 122     5    10  5 19  0.3805785595
## 123     5    11  5 18  0.0764874720
## 124     5    12  5 17  0.0385365145
## 125     5    13  5 16  0.1799387218
## 126     5    14  5 15  0.0224945319
## 127     5    15  5 14  0.2211758186
## 128     5    16  5 13  0.0464931690
## 129     5    17  5 12  0.1190013946
## 130     5    18  5 11  0.0634082237
## 131     5    19  5 10  0.1259628957
## 132     5    20  5  9  0.0412503828
## 133     5    21  5  8  0.1528295056
## 134     5    22  5  7  0.0804729901
## 135     5    23  5  6  0.0878024551
## 136     5    24  5  5  0.0221013123
## 137     5    25  5  4 -0.1580730750
## 138     5    26  5  3 -0.1525970876
## 139     5    27  5  2  0.0093442176
## 140     5    28  5  1 -0.0216219481
## 141     6     1  6 28  0.5330020838
## 142     6     2  6 27  0.8937678624
## 143     6     3  6 26  0.2502371633
## 144     6     4  6 25  0.1725353173
## 145     6     5  6 24  0.6250684205
## 146     6     6  6 23  1.0000000000
## 147     6     7  6 22  0.2388304747
## 148     6     8  6 21  0.1698549292
## 149     6     9  6 20  0.3485564080
## 150     6    10  6 19  0.5794210496
## 151     6    11  6 18 -0.0019083734
## 152     6    12  6 17 -0.0357900861
## 153     6    13  6 16  0.1556295064
## 154     6    14  6 15  0.0309307828
## 155     6    15  6 14  0.2107298256
## 156     6    16  6 13  0.0149424150
## 157     6    17  6 12  0.1175050363
## 158     6    18  6 11  0.0590179320
## 159     6    19  6 10  0.0521980812
## 160     6    20  6  9  0.0111444822
## 161     6    21  6  8  0.1203579702
## 162     6    22  6  7  0.0432875759
## 163     6    23  6  6  0.0299375759
## 164     6    24  6  5 -0.0043651186
## 165     6    25  6  4 -0.1670254367
## 166     6    26  6  3 -0.1748785305
## 167     6    27  6  2  0.0465895202
## 168     6    28  6  1 -0.0194929715
## 169     7     1  7 28  0.2001354972
## 170     7     2  7 27  0.1817447400
## 171     7     3  7 26  0.8959386168
## 172     7     4  7 25  0.5985383711
## 173     7     5  7 24  0.2579271084
## 174     7     6  7 23  0.2388304747
## 175     7     7  7 22  1.0000000000
## 176     7     8  7 21  0.6380892586
## 177     7     9  7 20  0.1872819388
## 178     7    10  7 19  0.1896097700
## 179     7    11  7 18  0.4830477205
## 180     7    12  7 17  0.3309468365
## 181     7    13  7 16 -0.0616141205
## 182     7    14  7 15  0.1890489987
## 183     7    15  7 14 -0.0168875252
## 184     7    16  7 13  0.1978692055
## 185     7    17  7 12 -0.0522485407
## 186     7    18  7 11 -0.1235288541
## 187     7    19  7 10  0.0921456874
## 188     7    20  7  9  0.0822916717
## 189     7    21  7  8 -0.0424914317
## 190     7    22  7  7 -0.0918091091
## 191     7    23  7  6  0.0705100341
## 192     7    24  7  5  0.0496501377
## 193     7    25  7  4 -0.0689889830
## 194     7    26  7  3 -0.0640682492
## 195     7    27  7  2 -0.2208008368
## 196     7    28  7  1 -0.1407310317
## 197     8     1  8 28  0.1435928158
## 198     8     2  8 27  0.1496599211
## 199     8     3  8 26  0.5663426153
## 200     8     4  8 25  0.8931363557
## 201     8     5  8 24  0.1702415247
## 202     8     6  8 23  0.1698549292
## 203     8     7  8 22  0.6380892586
## 204     8     8  8 21  1.0000000000
## 205     8     9  8 20  0.1597150925
## 206     8    10  8 19  0.1439030047
## 207     8    11  8 18  0.2979037651
## 208     8    12  8 17  0.5094027930
## 209     8    13  8 16 -0.0929192495
## 210     8    14  8 15  0.1773220593
## 211     8    15  8 14 -0.0527009814
## 212     8    16  8 13  0.2135452467
## 213     8    17  8 12 -0.0529228599
## 214     8    18  8 11 -0.1336890839
## 215     8    19  8 10  0.0966855638
## 216     8    20  8  9  0.0870560456
## 217     8    21  8  8 -0.0454362591
## 218     8    22  8  7 -0.1215712837
## 219     8    23  8  6  0.1295632088
## 220     8    24  8  5  0.0956409959
## 221     8    25  8  4 -0.0664159780
## 222     8    26  8  3 -0.0541639701
## 223     8    27  8  2 -0.1174691687
## 224     8    28  8  1 -0.1059790901
## 225     9     1  9 28  0.3354543521
## 226     9     2  9 27  0.2554488792
## 227     9     3  9 26  0.1590998642
## 228     9     4  9 25  0.1471856123
## 229     9     5  9 24  0.5247650003
## 230     9     6  9 23  0.3485564080
## 231     9     7  9 22  0.1872819388
## 232     9     8  9 21  0.1597150925
## 233     9     9  9 20  1.0000000000
## 234     9    10  9 19  0.6191470969
## 235     9    11  9 18  0.0859932853
## 236     9    12  9 17  0.0417367652
## 237     9    13  9 16  0.1419664831
## 238     9    14  9 15  0.0054686458
## 239     9    15  9 14  0.2097957002
## 240     9    16  9 13  0.0252721962
## 241     9    17  9 12 -0.1020562553
## 242     9    18  9 11 -0.1186395098
## 243     9    19  9 10  0.0608246439
## 244     9    20  9  9  0.0298210746
## 245     9    21  9  8 -0.1084083893
## 246     9    22  9  7 -0.1559030703
## 247     9    23  9  6  0.0749823572
## 248     9    24  9  5  0.0417622743
## 249     9    25  9  4 -0.3477992065
## 250     9    26  9  3 -0.3497188671
## 251     9    27  9  2  0.0651652185
## 252     9    28  9  1  0.0206209253
## 253    10     1 10 28  0.2597103357
## 254    10     2 10 27  0.4330457188
## 255    10     3 10 26  0.1698065141
## 256    10     4 10 25  0.1171675558
## 257    10     5 10 24  0.3805785595
## 258    10     6 10 23  0.5794210496
## 259    10     7 10 22  0.1896097700
## 260    10     8 10 21  0.1439030047
## 261    10     9 10 20  0.6191470969
## 262    10    10 10 19  1.0000000000
## 263    10    11 10 18  0.0743799653
## 264    10    12 10 17  0.0147474504
## 265    10    13 10 16  0.1278645398
## 266    10    14 10 15 -0.0112827652
## 267    10    15 10 14  0.1996461297
## 268    10    16 10 13 -0.0085837441
## 269    10    17 10 12  0.0171695789
## 270    10    18 10 11 -0.0590937213
## 271    10    19 10 10 -0.0007143294
## 272    10    20 10  9  0.0046034169
## 273    10    21 10  8 -0.0054182146
## 274    10    22 10  7 -0.0935556206
## 275    10    23 10  6  0.0052799040
## 276    10    24 10  5  0.0144032307
## 277    10    25 10  4 -0.2849182341
## 278    10    26 10  3 -0.2845167070
## 279    10    27 10  2  0.0666776581
## 280    10    28 10  1  0.0241004025
## 281    11     1 11 28  0.0339825465
## 282    11     2 11 27 -0.0191448341
## 283    11     3 11 26  0.3206650488
## 284    11     4 11 25  0.1936097739
## 285    11     5 11 24  0.0764874720
## 286    11     6 11 23 -0.0019083734
## 287    11     7 11 22  0.4830477205
## 288    11     8 11 21  0.2979037651
## 289    11     9 11 20  0.0859932853
## 290    11    10 11 19  0.0743799653
## 291    11    11 11 18  1.0000000000
## 292    11    12 11 17  0.6010950199
## 293    11    13 11 16 -0.1096999984
## 294    11    14 11 15 -0.0566478929
## 295    11    15 11 14 -0.1213601214
## 296    11    16 11 13  0.0127400936
## 297    11    17 11 12 -0.1129386766
## 298    11    18 11 11 -0.1366713648
## 299    11    19 11 10 -0.1218097766
## 300    11    20 11  9 -0.1805984023
## 301    11    21 11  8 -0.1067886731
## 302    11    22 11  7 -0.0797302196
## 303    11    23 11  6 -0.1815602795
## 304    11    24 11  5 -0.2006820653
## 305    11    25 11  4 -0.0227356052
## 306    11    26 11  3  0.0522930226
## 307    11    27 11  2 -0.3104903887
## 308    11    28 11  1 -0.2326244050
## 309    12     1 12 28  0.0115115369
## 310    12     2 12 27 -0.0458137926
## 311    12     3 12 26  0.2306647722
## 312    12     4 12 25  0.3385740616
## 313    12     5 12 24  0.0385365145
## 314    12     6 12 23 -0.0357900861
## 315    12     7 12 22  0.3309468365
## 316    12     8 12 21  0.5094027930
## 317    12     9 12 20  0.0417367652
## 318    12    10 12 19  0.0147474504
## 319    12    11 12 18  0.6010950199
## 320    12    12 12 17  1.0000000000
## 321    12    13 12 16 -0.1716878628
## 322    12    14 12 15 -0.0715048828
## 323    12    15 12 14 -0.1574184841
## 324    12    16 12 13 -0.0017497619
## 325    12    17 12 12 -0.1060272012
## 326    12    18 12 11 -0.1854075649
## 327    12    19 12 10 -0.1603961469
## 328    12    20 12  9 -0.2107427792
## 329    12    21 12  8 -0.1057520576
## 330    12    22 12  7 -0.1371137804
## 331    12    23 12  6 -0.2003795899
## 332    12    24 12  5 -0.2248105336
## 333    12    25 12  4 -0.0066444241
## 334    12    26 12  3  0.0379774846
## 335    12    27 12  2 -0.2930187743
## 336    12    28 12  1 -0.2448286923
## 337    13     1 13 28  0.1851052787
## 338    13     2 13 27  0.1484617714
## 339    13     3 13 26 -0.0580876115
## 340    13     4 13 25 -0.0641605109
## 341    13     5 13 24  0.1799387218
## 342    13     6 13 23  0.1556295064
## 343    13     7 13 22 -0.0616141205
## 344    13     8 13 21 -0.0929192495
## 345    13     9 13 20  0.1419664831
## 346    13    10 13 19  0.1278645398
## 347    13    11 13 18 -0.1096999984
## 348    13    12 13 17 -0.1716878628
## 349    13    13 13 16  1.0000000000
## 350    13    14 13 15  0.0848943410
## 351    13    15 13 14  0.8793138776
## 352    13    16 13 13  0.0222895677
## 353    13    17 13 12  0.4140705483
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## 355    13    19 13 10  0.1832810251
## 356    13    20 13  9  0.1350308721
## 357    13    21 13  8  0.3822399327
## 358    13    22 13  7  0.5054902304
## 359    13    23 13  6  0.1849825451
## 360    13    24 13  5  0.1349478180
## 361    13    25 13  4 -0.2508751795
## 362    13    26 13  3 -0.4426263663
## 363    13    27 13  2  0.1267355271
## 364    13    28 13  1  0.1258749814
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## 366    14     2 14 27 -0.0044368247
## 367    14     3 14 26  0.2379255490
## 368    14     4 14 25  0.2569921303
## 369    14     5 14 24  0.0224945319
## 370    14     6 14 23  0.0309307828
## 371    14     7 14 22  0.1890489987
## 372    14     8 14 21  0.1773220593
## 373    14     9 14 20  0.0054686458
## 374    14    10 14 19 -0.0112827652
## 375    14    11 14 18 -0.0566478929
## 376    14    12 14 17 -0.0715048828
## 377    14    13 14 16  0.0848943410
## 378    14    14 14 15  1.0000000000
## 379    14    15 14 14  0.1156335737
## 380    14    16 14 13  0.8702559899
## 381    14    17 14 12  0.1008386271
## 382    14    18 14 11  0.1057984330
## 383    14    19 14 10  0.4196793658
## 384    14    20 14  9  0.6807836535
## 385    14    21 14  8  0.0946190899
## 386    14    22 14  7  0.1085440179
## 387    14    23 14  6  0.4044773118
## 388    14    24 14  5  0.5671230842
## 389    14    25 14  4  0.0003007670
## 390    14    26 14  3 -0.0210608348
## 391    14    27 14  2 -0.1152049298
## 392    14    28 14  1 -0.2370428173
## 393    15     1 15 28  0.1746626000
## 394    15     2 15 27  0.1617019942
## 395    15     3 15 26 -0.0337875894
## 396    15     4 15 25 -0.0302412060
## 397    15     5 15 24  0.2211758186
## 398    15     6 15 23  0.2107298256
## 399    15     7 15 22 -0.0168875252
## 400    15     8 15 21 -0.0527009814
## 401    15     9 15 20  0.2097957002
## 402    15    10 15 19  0.1996461297
## 403    15    11 15 18 -0.1213601214
## 404    15    12 15 17 -0.1574184841
## 405    15    13 15 16  0.8793138776
## 406    15    14 15 15  0.1156335737
## 407    15    15 15 14  1.0000000000
## 408    15    16 15 13  0.0438837862
## 409    15    17 15 12  0.3976691556
## 410    15    18 15 11  0.5542317940
## 411    15    19 15 10  0.1909066525
## 412    15    20 15  9  0.1630639166
## 413    15    21 15  8  0.3577842799
## 414    15    22 15  7  0.4490303737
## 415    15    23 15  6  0.1937408697
## 416    15    24 15  5  0.1594272205
## 417    15    25 15  4 -0.3665807721
## 418    15    26 15  3 -0.6144718038
## 419    15    27 15  2  0.1201383559
## 420    15    28 15  1  0.1312946007
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## 422    16     2 16 27 -0.0207708897
## 423    16     3 16 26  0.1734177768
## 424    16     4 16 25  0.2311232770
## 425    16     5 16 24  0.0464931690
## 426    16     6 16 23  0.0149424150
## 427    16     7 16 22  0.1978692055
## 428    16     8 16 21  0.2135452467
## 429    16     9 16 20  0.0252721962
## 430    16    10 16 19 -0.0085837441
## 431    16    11 16 18  0.0127400936
## 432    16    12 16 17 -0.0017497619
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## 435    16    15 16 14  0.0438837862
## 436    16    16 16 13  1.0000000000
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## 440    16    20 16  9  0.6349284280
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## 448    16    28 16  1 -0.3912590167
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## 450    17     2 17 27  0.1366150760
## 451    17     3 17 26 -0.0051049154
## 452    17     4 17 25 -0.0165031044
## 453    17     5 17 24  0.1190013946
## 454    17     6 17 23  0.1175050363
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## 456    17     8 17 21 -0.0529228599
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## 458    17    10 17 19  0.0171695789
## 459    17    11 17 18 -0.1129386766
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## 461    17    13 17 16  0.4140705483
## 462    17    14 17 15  0.1008386271
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## 465    17    17 17 12  1.0000000000
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## 467    17    19 17 10  0.1306260892
## 468    17    20 17  9  0.0871468633
## 469    17    21 17  8  0.8928450714
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## 471    17    23 17  6  0.0868636416
## 472    17    24 17  5  0.0332481781
## 473    17    25 17  4  0.2405338214
## 474    17    26 17  3  0.0770003836
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## 480    18     4 18 25 -0.0942151651
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## 548    20    16 20 13  0.6349284280
## 549    20    17 20 12  0.0871468633
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## 557    20    25 20  4 -0.0493096149
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## 579    21    19 21 10  0.1205029250
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## 581    21    21 21  8  1.0000000000
## 582    21    22 21  7  0.6317565550
## 583    21    23 21  6  0.0661950235
## 584    21    24 21  5  0.0622222427
## 585    21    25 21  4  0.4130309353
## 586    21    26 21  3  0.1960988576
## 587    21    27 21  2 -0.0040007136
## 588    21    28 21  1  0.0349029400
## 589    22     1 22 28  0.1268074199
## 590    22     2 22 27  0.0741686136
## 591    22     3 22 26 -0.0804844646
## 592    22     4 22 25 -0.1006498834
## 593    22     5 22 24  0.0804729901
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## 595    22     7 22 22 -0.0918091091
## 596    22     8 22 21 -0.1215712837
## 597    22     9 22 20 -0.1559030703
## 598    22    10 22 19 -0.0935556206
## 599    22    11 22 18 -0.0797302196
## 600    22    12 22 17 -0.1371137804
## 601    22    13 22 16  0.5054902304
## 602    22    14 22 15  0.1085440179
## 603    22    15 22 14  0.4490303737
## 604    22    16 22 13  0.0551186893
## 605    22    17 22 12  0.5424748169
## 606    22    18 22 11  0.8553355845
## 607    22    19 22 10  0.1176090896
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## 611    22    23 22  6  0.1142026886
## 612    22    24 22  5  0.1161500321
## 613    22    25 22  4  0.3367125611
## 614    22    26 22  3  0.4290104551
## 615    22    27 22  2  0.0333868119
## 616    22    28 22  1  0.0730219030
## 617    23     1 23 28  0.0573609285
## 618    23     2 23 27  0.0098690056
## 619    23     3 23 26  0.1024635727
## 620    23     4 23 25  0.1703589375
## 621    23     5 23 24  0.0878024551
## 622    23     6 23 23  0.0299375759
## 623    23     7 23 22  0.0705100341
## 624    23     8 23 21  0.1295632088
## 625    23     9 23 20  0.0749823572
## 626    23    10 23 19  0.0052799040
## 627    23    11 23 18 -0.1815602795
## 628    23    12 23 17 -0.2003795899
## 629    23    13 23 16  0.1849825451
## 630    23    14 23 15  0.4044773118
## 631    23    15 23 14  0.1937408697
## 632    23    16 23 13  0.3755354646
## 633    23    17 23 12  0.0868636416
## 634    23    18 23 11  0.1649781165
## 635    23    19 23 10  0.8631332985
## 636    23    20 23  9  0.6471309061
## 637    23    21 23  8  0.0661950235
## 638    23    22 23  7  0.1142026886
## 639    23    23 23  6  1.0000000000
## 640    23    24 23  5  0.7274828132
## 641    23    25 23  4 -0.1213241455
## 642    23    26 23  3 -0.0950664922
## 643    23    27 23  2  0.5184734046
## 644    23    28 23  1  0.4270089413
## 645    24     1 24 28  0.0078757829
## 646    24     2 24 27 -0.0407126065
## 647    24     3 24 26  0.0504413323
## 648    24     4 24 25  0.1470004360
## 649    24     5 24 24  0.0221013123
## 650    24     6 24 23 -0.0043651186
## 651    24     7 24 22  0.0496501377
## 652    24     8 24 21  0.0956409959
## 653    24     9 24 20  0.0417622743
## 654    24    10 24 19  0.0144032307
## 655    24    11 24 18 -0.2006820653
## 656    24    12 24 17 -0.2248105336
## 657    24    13 24 16  0.1349478180
## 658    24    14 24 15  0.5671230842
## 659    24    15 24 14  0.1594272205
## 660    24    16 24 13  0.5432329871
## 661    24    17 24 12  0.0332481781
## 662    24    18 24 11  0.1003632799
## 663    24    19 24 10  0.6109065361
## 664    24    20 24  9  0.8762268253
## 665    24    21 24  8  0.0622222427
## 666    24    22 24  7  0.1161500321
## 667    24    23 24  6  0.7274828132
## 668    24    24 24  5  1.0000000000
## 669    24    25 24  4 -0.0555128930
## 670    24    26 24  3 -0.0587289265
## 671    24    27 24  2  0.3754038999
## 672    24    28 24  1  0.5601035545
## 673    25     1 25 28 -0.0821143751
## 674    25     2 25 27 -0.1266538151
## 675    25     3 25 26 -0.0137023668
## 676    25     4 25 25 -0.0438218586
## 677    25     5 25 24 -0.1580730750
## 678    25     6 25 23 -0.1670254367
## 679    25     7 25 22 -0.0689889830
## 680    25     8 25 21 -0.0664159780
## 681    25     9 25 20 -0.3477992065
## 682    25    10 25 19 -0.2849182341
## 683    25    11 25 18 -0.0227356052
## 684    25    12 25 17 -0.0066444241
## 685    25    13 25 16 -0.2508751795
## 686    25    14 25 15  0.0003007670
## 687    25    15 25 14 -0.3665807721
## 688    25    16 25 13  0.0261707885
## 689    25    17 25 12  0.2405338214
## 690    25    18 25 11  0.2016749096
## 691    25    19 25 10 -0.0878578147
## 692    25    20 25  9 -0.0493096149
## 693    25    21 25  8  0.4130309353
## 694    25    22 25  7  0.3367125611
## 695    25    23 25  6 -0.1213241455
## 696    25    24 25  5 -0.0555128930
## 697    25    25 25  4  1.0000000000
## 698    25    26 25  3  0.6679274700
## 699    25    27 25  2 -0.1067047814
## 700    25    28 25  1 -0.0866289821
## 701    26     1 26 28 -0.0647178269
## 702    26     2 26 27 -0.0981254222
## 703    26     3 26 26 -0.0369701789
## 704    26     4 26 25 -0.0584066354
## 705    26     5 26 24 -0.1525970876
## 706    26     6 26 23 -0.1748785305
## 707    26     7 26 22 -0.0640682492
## 708    26     8 26 21 -0.0541639701
## 709    26     9 26 20 -0.3497188671
## 710    26    10 26 19 -0.2845167070
## 711    26    11 26 18  0.0522930226
## 712    26    12 26 17  0.0379774846
## 713    26    13 26 16 -0.4426263663
## 714    26    14 26 15 -0.0210608348
## 715    26    15 26 14 -0.6144718038
## 716    26    16 26 13  0.0043049811
## 717    26    17 26 12  0.0770003836
## 718    26    18 26 11  0.1949284414
## 719    26    19 26 10 -0.0891214805
## 720    26    20 26  9 -0.0531370303
## 721    26    21 26  8  0.1960988576
## 722    26    22 26  7  0.4290104551
## 723    26    23 26  6 -0.0950664922
## 724    26    24 26  5 -0.0587289265
## 725    26    25 26  4  0.6679274700
## 726    26    26 26  3  1.0000000000
## 727    26    27 26  2 -0.0921071767
## 728    26    28 26  1 -0.0683809336
## 729    27     1 27 28 -0.0192608529
## 730    27     2 27 27  0.0479248469
## 731    27     3 27 26 -0.1328173925
## 732    27     4 27 25 -0.0334908731
## 733    27     5 27 24  0.0093442176
## 734    27     6 27 23  0.0465895202
## 735    27     7 27 22 -0.2208008368
## 736    27     8 27 21 -0.1174691687
## 737    27     9 27 20  0.0651652185
## 738    27    10 27 19  0.0666776581
## 739    27    11 27 18 -0.3104903887
## 740    27    12 27 17 -0.2930187743
## 741    27    13 27 16  0.1267355271
## 742    27    14 27 15 -0.1152049298
## 743    27    15 27 14  0.1201383559
## 744    27    16 27 13 -0.2427214013
## 745    27    17 27 12  0.0016191206
## 746    27    18 27 11  0.0822511915
## 747    27    19 27 10  0.3430005340
## 748    27    20 27  9  0.2692215108
## 749    27    21 27  8 -0.0040007136
## 750    27    22 27  7  0.0333868119
## 751    27    23 27  6  0.5184734046
## 752    27    24 27  5  0.3754038999
## 753    27    25 27  4 -0.1067047814
## 754    27    26 27  3 -0.0921071767
## 755    27    27 27  2  1.0000000000
## 756    27    28 27  1  0.6510395972
## 757    28     1 28 28 -0.0385099639
## 758    28     2 28 27 -0.0240982679
## 759    28     3 28 26 -0.1156632887
## 760    28     4 28 25 -0.0670002102
## 761    28     5 28 24 -0.0216219481
## 762    28     6 28 23 -0.0194929715
## 763    28     7 28 22 -0.1407310317
## 764    28     8 28 21 -0.1059790901
## 765    28     9 28 20  0.0206209253
## 766    28    10 28 19  0.0241004025
## 767    28    11 28 18 -0.2326244050
## 768    28    12 28 17 -0.2448286923
## 769    28    13 28 16  0.1258749814
## 770    28    14 28 15 -0.2370428173
## 771    28    15 28 14  0.1312946007
## 772    28    16 28 13 -0.3912590167
## 773    28    17 28 12  0.0043210264
## 774    28    18 28 11  0.0685096139
## 775    28    19 28 10  0.2866485245
## 776    28    20 28  9  0.3339269840
## 777    28    21 28  8  0.0349029400
## 778    28    22 28  7  0.0730219030
## 779    28    23 28  6  0.4270089413
## 780    28    24 28  5  0.5601035545
## 781    28    25 28  4 -0.0866289821
## 782    28    26 28  3 -0.0683809336
## 783    28    27 28  2  0.6510395972
## 784    28    28 28  1  1.0000000000
## 
## $arg
## $arg$type
## [1] "full"

3.1.4 Pairplots

Distribution and plots of data points between two variables for NAcc and Insula pairs.

ggpairs(abcd_df[,nacc_pairs]) + theme_minimal()

ggpairs(abcd_df[,insula_pairs]) + theme_minimal()

3.1.5 Bivariate: r > .85

Check if any and which exceed r > .85

# rerun to have original names: 
abcd_cor = cor(abcd_df[,mod_vars]) 

# Diagonal are all 1's, convert to 0 to avoid confusion
diag(abcd_cor) <- 0

# Find indices of correlations exceeding 0.84 on in upper.tri or lower.tri (otherwise redundant)
abcd_high_index <- which(abcd_cor > 0.85 | abcd_cor < -0.85, arr.ind = TRUE)

# Print the correlations that exceed 0.84
abcdcor_rownames = row.names(abcd_cor)
abcdcor_colnames = colnames(abcd_cor)

# loop through which indices exceed the corr, print value and save name to list
n1_exceed = 0
abcd_exceedlist = list()
for (i in 1:nrow(abcd_high_index)) {
  n1_exceed = n1_exceed+1
  row <- abcd_high_index[i, 1]
  col <- abcd_high_index[i, 2]
  correlation <- abcd_cor[row, col]
  print(paste(n1_exceed,"-", abcdcor_rownames[row], "~", abcdcor_colnames[col], "r:", round(correlation,3)))
  abcd_exceedlist[n1_exceed] <- paste(abcdcor_rownames[row], "~", abcdcor_colnames[col])
}

## [1] "1 - BWin_v_Neut_L_NAc_r1 ~ AWin_v_Neut_L_NAc_r1 r: 0.885"
## [1] "2 - BWin_v_Neut_R_NAc_r1 ~ AWin_v_Neut_R_NAc_r1 r: 0.894"
## [1] "3 - BWin_v_Neut_L_NAc_r2 ~ AWin_v_Neut_L_NAc_r2 r: 0.896"
## [1] "4 - BWin_v_Neut_R_NAc_r2 ~ AWin_v_Neut_R_NAc_r2 r: 0.893"
## [1] "5 - AWin_v_Neut_L_NAc_r1 ~ BWin_v_Neut_L_NAc_r1 r: 0.885"
## [1] "6 - AWin_v_Neut_R_NAc_r1 ~ BWin_v_Neut_R_NAc_r1 r: 0.894"
## [1] "7 - AWin_v_Neut_L_NAc_r2 ~ BWin_v_Neut_L_NAc_r2 r: 0.896"
## [1] "8 - AWin_v_Neut_R_NAc_r2 ~ BWin_v_Neut_R_NAc_r2 r: 0.893"
## [1] "9 - BWin_v_Neut_R_Ins_r1 ~ AWin_v_Neut_R_Ins_r1 r: 0.879"
## [1] "10 - BWin_v_Neut_R_Ins_r2 ~ AWin_v_Neut_R_Ins_r2 r: 0.87"
## [1] "11 - AWin_v_Neut_R_Ins_r1 ~ BWin_v_Neut_R_Ins_r1 r: 0.879"
## [1] "12 - AWin_v_Neut_R_Ins_r2 ~ BWin_v_Neut_R_Ins_r2 r: 0.87"
## [1] "13 - BLose_v_Neut_L_Ins_r1 ~ ALose_v_Neut_L_Ins_r1 r: 0.893"
## [1] "14 - BLose_v_Neut_R_Ins_r1 ~ ALose_v_Neut_R_Ins_r1 r: 0.855"
## [1] "15 - BLose_v_Neut_L_Ins_r2 ~ ALose_v_Neut_L_Ins_r2 r: 0.863"
## [1] "16 - BLose_v_Neut_R_Ins_r2 ~ ALose_v_Neut_R_Ins_r2 r: 0.876"
## [1] "17 - ALose_v_Neut_L_Ins_r1 ~ BLose_v_Neut_L_Ins_r1 r: 0.893"
## [1] "18 - ALose_v_Neut_R_Ins_r1 ~ BLose_v_Neut_R_Ins_r1 r: 0.855"
## [1] "19 - ALose_v_Neut_L_Ins_r2 ~ BLose_v_Neut_L_Ins_r2 r: 0.863"
## [1] "20 - ALose_v_Neut_R_Ins_r2 ~ BLose_v_Neut_R_Ins_r2 r: 0.876"

# after running, clean environment of uneccessary vars
rm(row,col,correlation,i)

Of the 378 unique correlations, the abcd study has 20 correlations that are r > .85

3.2 AHRB

Run the correlation matrix and plot heatmap. Then, check whether an correlations exceed the Stage 1 specificed > .85

3.2.1 Correlations

Plot correlation matrix only of Left/Right NAcc and Insula mean signal intensity values for Contrasts and Regions used in the MID population model. (Note: diagonal is set to 0)

ahrb_cor = cor(ahrb_df[,mod_vars]) 

# numeric+string style names for correlation table 
numstr_row <- row.names(ahrb_cor)
numstr_modrow_names <- paste0(1:28, "_", numstr_row)
numstr_col <- colnames(ahrb_cor)
numstr_modcol_names <- paste0(1:28, "_", numstr_col)

# Create table
row.names(ahrb_cor) <- numstr_modrow_names
colnames(ahrb_cor) <- numstr_modcol_names
kable(as.data.frame(ahrb_cor), booktabs = TRUE) %>%
  kable_styling(font_size = 8,position = 'center')

	1_AWin_v_Neut_L_NAc_r1	2_AWin_v_Neut_R_NAc_r1	3_AWin_v_Neut_L_NAc_r2	4_AWin_v_Neut_R_NAc_r2	5_BWin_v_Neut_L_NAc_r1	6_BWin_v_Neut_R_NAc_r1	7_BWin_v_Neut_L_NAc_r2	8_BWin_v_Neut_R_NAc_r2	9_BWin_v_BLose_L_NAc_r1	10_BWin_v_BLose_R_NAc_r1	11_BWin_v_BLose_L_NAc_r2	12_BWin_v_BLose_R_NAc_r2	13_AWin_v_Neut_R_Ins_r1	14_AWin_v_Neut_R_Ins_r2	15_BWin_v_Neut_R_Ins_r1	16_BWin_v_Neut_R_Ins_r2	17_ALose_v_Neut_L_Ins_r1	18_ALose_v_Neut_R_Ins_r1	19_ALose_v_Neut_L_Ins_r2	20_ALose_v_Neut_R_Ins_r2	21_BLose_v_Neut_L_Ins_r1	22_BLose_v_Neut_R_Ins_r1	23_BLose_v_Neut_L_Ins_r2	24_BLose_v_Neut_R_Ins_r2	25_BLose_v_BWin_L_Ins_r1	26_BLose_v_BWin_R_Ins_r1	27_BLose_v_BWin_L_Ins_r2	28_BLose_v_BWin_R_Ins_r2
1_AWin_v_Neut_L_NAc_r1	1.0000000	0.4903278	-0.0296080	-0.0386324	0.8754663	0.4107293	-0.0121012	-0.0575760	0.1689798	0.0971350	-0.0326796	-0.0108420	0.1672593	-0.0446503	0.0765127	-0.0328314	0.0664330	0.1229140	-0.1675437	-0.0870161	-0.0220042	0.1082580	-0.1309481	-0.0742043	-0.0597079	0.0456917	-0.0868043	-0.0481130
2_AWin_v_Neut_R_NAc_r1	0.4903278	1.0000000	0.0225056	-0.0324984	0.4618953	0.8383800	0.0771671	-0.0001852	0.0968810	0.2737311	0.1935326	0.1628689	0.2625986	0.1288952	0.2135139	0.1086315	0.1058152	0.2208955	-0.1459135	-0.0023833	0.0192819	0.1835667	-0.2013348	-0.0099951	-0.0849256	-0.0165200	-0.1486100	-0.1440584
3_AWin_v_Neut_L_NAc_r2	-0.0296080	0.0225056	1.0000000	0.4794485	0.0755493	0.0773710	0.8794367	0.5418058	0.0449448	0.0255678	0.3534215	0.1932176	0.0318544	0.1615955	0.0456515	0.2535072	-0.0828886	-0.0417445	0.1253867	0.1663483	-0.1224842	-0.1066644	0.1399250	0.1467097	-0.0726466	-0.1804099	-0.2260960	-0.1338835
4_AWin_v_Neut_R_NAc_r2	-0.0386324	-0.0324984	0.4794485	1.0000000	-0.0705427	-0.0145433	0.3667614	0.8565686	-0.1216178	0.0485687	0.1497357	0.3309734	0.1035345	0.3166805	-0.0013440	0.3528525	-0.0297701	0.0105393	0.0406229	0.2590484	0.0306158	0.0210709	0.0325546	0.1607037	0.0551774	0.0264752	-0.3502396	-0.2375232
5_BWin_v_Neut_L_NAc_r1	0.8754663	0.4618953	0.0755493	-0.0705427	1.0000000	0.5335054	0.1224293	-0.0355665	0.3387879	0.2470884	0.0974365	-0.0512346	0.2243150	0.0714286	0.1662141	0.1052248	0.1446782	0.1709500	-0.0076000	0.0520128	0.0407811	0.1259435	-0.0306898	0.0124099	-0.0537657	-0.0328760	-0.1576199	-0.1130837
6_BWin_v_Neut_R_NAc_r1	0.4107293	0.8383800	0.0773710	-0.0145433	0.5335054	1.0000000	0.1263809	0.0560763	0.3088430	0.5758382	0.2026716	0.1083443	0.2362318	0.2084450	0.2668695	0.1608475	0.1111757	0.2301260	-0.0162269	0.1170235	0.0114014	0.1697059	-0.0962809	0.0580406	-0.1026088	-0.0926595	-0.0993836	-0.1266386
7_BWin_v_Neut_L_NAc_r2	-0.0121012	0.0771671	0.8794367	0.3667614	0.1224293	0.1263809	1.0000000	0.5268166	0.0291828	0.0722738	0.5446382	0.2238332	0.1276447	0.1279515	0.1056359	0.2241835	-0.0042940	0.0501525	0.0823141	0.1791949	-0.0633459	-0.0378892	0.1198505	0.2027594	-0.0894330	-0.1640580	-0.1536852	-0.0318516
8_BWin_v_Neut_R_NAc_r2	-0.0575760	-0.0001852	0.5418058	0.8565686	-0.0355665	0.0560763	0.5268166	1.0000000	-0.0528787	0.0591757	0.2576585	0.5299906	0.1789324	0.3129800	0.0353034	0.3712303	0.0048286	0.0647423	0.0716039	0.2539869	0.0369270	0.0755215	0.0463032	0.1565911	0.0679960	0.0516705	-0.4020446	-0.2644627
9_BWin_v_BLose_L_NAc_r1	0.1689798	0.0968810	0.0449448	-0.1216178	0.3387879	0.3088430	0.0291828	-0.0528787	1.0000000	0.5834113	-0.1321983	-0.1045728	0.0992133	0.0716254	0.1881741	0.0992361	0.0761407	0.0833459	-0.0554745	-0.0341785	0.0074437	0.0433935	-0.0630413	-0.0581085	-0.1568150	-0.1572069	-0.0872897	-0.1889009
10_BWin_v_BLose_R_NAc_r1	0.0971350	0.2737311	0.0255678	0.0485687	0.2470884	0.5758382	0.0722738	0.0591757	0.5834113	1.0000000	0.0429314	0.0203397	0.0999224	0.2093690	0.1888358	0.2062535	0.1559652	0.1489925	0.1071630	0.1500816	0.0639472	0.0897461	0.1414913	0.1076469	-0.1319079	-0.1022821	-0.0254599	-0.1224704
11_BWin_v_BLose_L_NAc_r2	-0.0326796	0.1935326	0.3534215	0.1497357	0.0974365	0.2026716	0.5446382	0.2576585	-0.1321983	0.0429314	1.0000000	0.4446902	-0.0006057	0.1964935	0.0203629	0.2266210	-0.0209663	0.0082995	-0.0251049	0.1261361	-0.0713554	-0.0532677	-0.0457367	0.1690758	-0.0934297	-0.0870379	-0.1089879	-0.0747406
12_BWin_v_BLose_R_NAc_r2	-0.0108420	0.1628689	0.1932176	0.3309734	-0.0512346	0.1083443	0.2238332	0.5299906	-0.1045728	0.0203397	0.4446902	1.0000000	0.0169767	0.2365435	0.0027480	0.2411308	-0.0174739	-0.0094964	-0.0401406	0.0811555	0.0077792	0.0265168	-0.0700521	0.0762104	-0.0316686	0.0291163	-0.2153809	-0.2019748
13_AWin_v_Neut_R_Ins_r1	0.1672593	0.2625986	0.0318544	0.1035345	0.2243150	0.2362318	0.1276447	0.1789324	0.0992133	0.0999224	-0.0006057	0.0169767	1.0000000	0.2159763	0.8500593	0.2184297	0.6177927	0.7985721	0.1980304	0.1843337	0.5342453	0.7198994	0.1246637	0.1733622	-0.0128889	-0.0787900	-0.2295665	-0.0595488
14_AWin_v_Neut_R_Ins_r2	-0.0446503	0.1288952	0.1615955	0.3166805	0.0714286	0.2084450	0.1279515	0.3129800	0.0716254	0.2093690	0.1964935	0.2365435	0.2159763	1.0000000	0.2135174	0.9032488	0.0832068	0.0408423	0.4640598	0.7195197	0.0317714	0.0474218	0.3985740	0.6296619	-0.1863559	-0.1810382	-0.3107470	-0.3502000
15_BWin_v_Neut_R_Ins_r1	0.0765127	0.2135139	0.0456515	-0.0013440	0.1662141	0.2668695	0.1056359	0.0353034	0.1881741	0.1888358	0.0203629	0.0027480	0.8500593	0.2135174	1.0000000	0.2406020	0.5023449	0.7020383	0.1997774	0.1636880	0.4348258	0.6328427	0.1714277	0.1704713	-0.2096017	-0.3514247	-0.1718319	-0.0898883
16_BWin_v_Neut_R_Ins_r2	-0.0328314	0.1086315	0.2535072	0.3528525	0.1052248	0.1608475	0.2241835	0.3712303	0.0992361	0.2062535	0.2266210	0.2411308	0.2184297	0.9032488	0.2406020	1.0000000	0.1193623	0.0514160	0.4461404	0.6980826	0.0757985	0.0617331	0.4464734	0.6526962	-0.1501519	-0.1939376	-0.4183906	-0.4401722
17_ALose_v_Neut_L_Ins_r1	0.0664330	0.1058152	-0.0828886	-0.0297701	0.1446782	0.1111757	-0.0042940	0.0048286	0.0761407	0.1559652	-0.0209663	-0.0174739	0.6177927	0.0832068	0.5023449	0.1193623	1.0000000	0.6855655	0.2941090	0.1468413	0.8451421	0.5986553	0.1860388	0.0706214	0.2173371	0.1627671	-0.0690532	-0.0609093
18_ALose_v_Neut_R_Ins_r1	0.1229140	0.2208955	-0.0417445	0.0105393	0.1709500	0.2301260	0.0501525	0.0647423	0.0833459	0.1489925	0.0082995	-0.0094964	0.7985721	0.0408423	0.7020383	0.0514160	0.6855655	1.0000000	0.1911398	0.1013637	0.5987184	0.9074123	0.1165472	0.0819306	0.2074158	0.3132625	-0.0788968	0.0345380
19_ALose_v_Neut_L_Ins_r2	-0.1675437	-0.1459135	0.1253867	0.0406229	-0.0076000	-0.0162269	0.0823141	0.0716039	-0.0554745	0.1071630	-0.0251049	-0.0401406	0.1980304	0.4640598	0.1997774	0.4461404	0.2941090	0.1911398	1.0000000	0.6790522	0.2329720	0.1887130	0.8526879	0.5733988	0.0238475	0.0050619	0.1045047	0.1379641
20_ALose_v_Neut_R_Ins_r2	-0.0870161	-0.0023833	0.1663483	0.2590484	0.0520128	0.1170235	0.1791949	0.2539869	-0.0341785	0.1500816	0.1261361	0.0811555	0.1843337	0.7195197	0.1636880	0.6980826	0.1468413	0.1013637	0.6790522	1.0000000	0.0606278	0.1250449	0.5964041	0.8711466	-0.0807807	-0.0314410	0.0390552	0.1852649
21_BLose_v_Neut_L_Ins_r1	-0.0220042	0.0192819	-0.1224842	0.0306158	0.0407811	0.0114014	-0.0633459	0.0369270	0.0074437	0.0639472	-0.0713554	0.0077792	0.5342453	0.0317714	0.4348258	0.0757985	0.8451421	0.5987184	0.2329720	0.0606278	1.0000000	0.6461363	0.1109026	-0.0043701	0.4635688	0.2956323	-0.0850896	-0.0971753
22_BLose_v_Neut_R_Ins_r1	0.1082580	0.1835667	-0.1066644	0.0210709	0.1259435	0.1697059	-0.0378892	0.0755215	0.0433935	0.0897461	-0.0532677	0.0265168	0.7198994	0.0474218	0.6328427	0.0617331	0.5986553	0.9074123	0.1887130	0.1250449	0.6461363	1.0000000	0.1044008	0.0952389	0.3054747	0.5024930	-0.0474900	0.0376736
23_BLose_v_Neut_L_Ins_r2	-0.1309481	-0.2013348	0.1399250	0.0325546	-0.0306898	-0.0962809	0.1198505	0.0463032	-0.0630413	0.1414913	-0.0457367	-0.0700521	0.1246637	0.3985740	0.1714277	0.4464734	0.1860388	0.1165472	0.8526879	0.5964041	0.1109026	0.1044008	1.0000000	0.6422402	-0.0600957	-0.0654325	0.2614143	0.2192923
24_BLose_v_Neut_R_Ins_r2	-0.0742043	-0.0099951	0.1467097	0.1607037	0.0124099	0.0580406	0.2027594	0.1565911	-0.0581085	0.1076469	0.1690758	0.0762104	0.1733622	0.6296619	0.1704713	0.6526962	0.0706214	0.0819306	0.5733988	0.8711466	-0.0043701	0.0952389	0.6422402	1.0000000	-0.1274574	-0.0751448	0.1668478	0.3929735
25_BLose_v_BWin_L_Ins_r1	-0.0597079	-0.0849256	-0.0726466	0.0551774	-0.0537657	-0.1026088	-0.0894330	0.0679960	-0.1568150	-0.1319079	-0.0934297	-0.0316686	-0.0128889	-0.1863559	-0.2096017	-0.1501519	0.2173371	0.2074158	0.0238475	-0.0807807	0.4635688	0.3054747	-0.0600957	-0.1274574	1.0000000	0.6031709	0.0205188	0.0309552
26_BLose_v_BWin_R_Ins_r1	0.0456917	-0.0165200	-0.1804099	0.0264752	-0.0328760	-0.0926595	-0.1640580	0.0516705	-0.1572069	-0.1022821	-0.0870379	0.0291163	-0.0787900	-0.1810382	-0.3514247	-0.1939376	0.1627671	0.3132625	0.0050619	-0.0314410	0.2956323	0.5024930	-0.0654325	-0.0751448	0.6031709	1.0000000	0.1343524	0.1458854
27_BLose_v_BWin_L_Ins_r2	-0.0868043	-0.1486100	-0.2260960	-0.3502396	-0.1576199	-0.0993836	-0.1536852	-0.4020446	-0.0872897	-0.0254599	-0.1089879	-0.2153809	-0.2295665	-0.3107470	-0.1718319	-0.4183906	-0.0690532	-0.0788968	0.1045047	0.0390552	-0.0850896	-0.0474900	0.2614143	0.1668478	0.0205188	0.1343524	1.0000000	0.7052694
28_BLose_v_BWin_R_Ins_r2	-0.0481130	-0.1440584	-0.1338835	-0.2375232	-0.1130837	-0.1266386	-0.0318516	-0.2644627	-0.1889009	-0.1224704	-0.0747406	-0.2019748	-0.0595488	-0.3502000	-0.0898883	-0.4401722	-0.0609093	0.0345380	0.1379641	0.1852649	-0.0971753	0.0376736	0.2192923	0.3929735	0.0309552	0.1458854	0.7052694	1.0000000

# Numeric only for plot
numeric_row <- paste0(1:nrow(ahrb_cor))
numeric_col <- paste0(1:nrow(ahrb_cor))
rownames(ahrb_cor) <- numeric_row
colnames(ahrb_cor) <- numeric_col

ab_cor_plt <- corrplot(ahrb_cor , method = "color", tl.cex = .6, diag = TRUE)

ab_cor_plt

## $corr
##              1             2           3            4           5           6
## 1   1.00000000  0.4903277676 -0.02960800 -0.038632409  0.87546630  0.41072928
## 2   0.49032777  1.0000000000  0.02250563 -0.032498384  0.46189531  0.83838003
## 3  -0.02960800  0.0225056320  1.00000000  0.479448469  0.07554927  0.07737101
## 4  -0.03863241 -0.0324983841  0.47944847  1.000000000 -0.07054274 -0.01454326
## 5   0.87546630  0.4618953067  0.07554927 -0.070542741  1.00000000  0.53350539
## 6   0.41072928  0.8383800268  0.07737101 -0.014543255  0.53350539  1.00000000
## 7  -0.01210123  0.0771671196  0.87943672  0.366761402  0.12242929  0.12638092
## 8  -0.05757596 -0.0001852317  0.54180583  0.856568617 -0.03556646  0.05607628
## 9   0.16897982  0.0968810347  0.04494478 -0.121617763  0.33878794  0.30884296
## 10  0.09713504  0.2737310777  0.02556776  0.048568728  0.24708845  0.57583821
## 11 -0.03267956  0.1935325979  0.35342150  0.149735723  0.09743646  0.20267164
## 12 -0.01084205  0.1628688913  0.19321756  0.330973415 -0.05123461  0.10834428
## 13  0.16725929  0.2625986004  0.03185438  0.103534468  0.22431497  0.23623180
## 14 -0.04465031  0.1288951950  0.16159554  0.316680461  0.07142860  0.20844499
## 15  0.07651273  0.2135139150  0.04565148 -0.001343961  0.16621410  0.26686950
## 16 -0.03283137  0.1086315041  0.25350717  0.352852547  0.10522477  0.16084750
## 17  0.06643305  0.1058151605 -0.08288862 -0.029770073  0.14467822  0.11117573
## 18  0.12291404  0.2208954877 -0.04174453  0.010539309  0.17095000  0.23012596
## 19 -0.16754367 -0.1459135036  0.12538673  0.040622896 -0.00760001 -0.01622687
## 20 -0.08701606 -0.0023832646  0.16634830  0.259048446  0.05201283  0.11702354
## 21 -0.02200424  0.0192819295 -0.12248416  0.030615829  0.04078110  0.01140136
## 22  0.10825797  0.1835667242 -0.10666437  0.021070898  0.12594352  0.16970594
## 23 -0.13094810 -0.2013348159  0.13992502  0.032554557 -0.03068982 -0.09628085
## 24 -0.07420429 -0.0099951034  0.14670971  0.160703659  0.01240994  0.05804059
## 25 -0.05970792 -0.0849256090 -0.07264656  0.055177372 -0.05376574 -0.10260885
## 26  0.04569165 -0.0165200108 -0.18040993  0.026475225 -0.03287598 -0.09265947
## 27 -0.08680434 -0.1486100483 -0.22609597 -0.350239639 -0.15761990 -0.09938359
## 28 -0.04811295 -0.1440583873 -0.13388354 -0.237523231 -0.11308366 -0.12663860
##               7             8            9          10           11
## 1  -0.012101228 -0.0575759630  0.168979818  0.09713504 -0.032679564
## 2   0.077167120 -0.0001852317  0.096881035  0.27373108  0.193532598
## 3   0.879436719  0.5418058338  0.044944779  0.02556776  0.353421499
## 4   0.366761402  0.8565686170 -0.121617763  0.04856873  0.149735723
## 5   0.122429290 -0.0355664584  0.338787944  0.24708845  0.097436463
## 6   0.126380918  0.0560762755  0.308842963  0.57583821  0.202671638
## 7   1.000000000  0.5268166109  0.029182781  0.07227381  0.544638173
## 8   0.526816611  1.0000000000 -0.052878748  0.05917574  0.257658495
## 9   0.029182781 -0.0528787476  1.000000000  0.58341125 -0.132198262
## 10  0.072273806  0.0591757366  0.583411253  1.00000000  0.042931373
## 11  0.544638173  0.2576584946 -0.132198262  0.04293137  1.000000000
## 12  0.223833186  0.5299905857 -0.104572832  0.02033968  0.444690169
## 13  0.127644656  0.1789324080  0.099213257  0.09992243 -0.000605743
## 14  0.127951534  0.3129800117  0.071625385  0.20936899  0.196493535
## 15  0.105635929  0.0353034312  0.188174111  0.18883579  0.020362853
## 16  0.224183485  0.3712302520  0.099236093  0.20625355  0.226621033
## 17 -0.004293978  0.0048286312  0.076140700  0.15596518 -0.020966342
## 18  0.050152464  0.0647422601  0.083345915  0.14899246  0.008299474
## 19  0.082314072  0.0716039067 -0.055474452  0.10716304 -0.025104914
## 20  0.179194861  0.2539868541 -0.034178520  0.15008164  0.126136088
## 21 -0.063345918  0.0369269720  0.007443732  0.06394718 -0.071355389
## 22 -0.037889170  0.0755215239  0.043393542  0.08974615 -0.053267702
## 23  0.119850464  0.0463031527 -0.063041342  0.14149129 -0.045736688
## 24  0.202759444  0.1565911367 -0.058108544  0.10764687  0.169075753
## 25 -0.089432995  0.0679959988 -0.156815008 -0.13190787 -0.093429665
## 26 -0.164057981  0.0516705482 -0.157206925 -0.10228214 -0.087037877
## 27 -0.153685153 -0.4020445744 -0.087289730 -0.02545992 -0.108987852
## 28 -0.031851608 -0.2644627015 -0.188900867 -0.12247043 -0.074740643
##              12           13          14           15          16           17
## 1  -0.010842045  0.167259286 -0.04465031  0.076512729 -0.03283137  0.066433050
## 2   0.162868891  0.262598600  0.12889519  0.213513915  0.10863150  0.105815160
## 3   0.193217563  0.031854379  0.16159554  0.045651484  0.25350717 -0.082888622
## 4   0.330973415  0.103534468  0.31668046 -0.001343961  0.35285255 -0.029770073
## 5  -0.051234615  0.224314968  0.07142860  0.166214098  0.10522477  0.144678225
## 6   0.108344284  0.236231800  0.20844499  0.266869500  0.16084750  0.111175732
## 7   0.223833186  0.127644656  0.12795153  0.105635929  0.22418348 -0.004293978
## 8   0.529990586  0.178932408  0.31298001  0.035303431  0.37123025  0.004828631
## 9  -0.104572832  0.099213257  0.07162538  0.188174111  0.09923609  0.076140700
## 10  0.020339680  0.099922429  0.20936899  0.188835791  0.20625355  0.155965181
## 11  0.444690169 -0.000605743  0.19649353  0.020362853  0.22662103 -0.020966342
## 12  1.000000000  0.016976742  0.23654352  0.002747971  0.24113075 -0.017473878
## 13  0.016976742  1.000000000  0.21597625  0.850059287  0.21842965  0.617792671
## 14  0.236543516  0.215976253  1.00000000  0.213517435  0.90324875  0.083206835
## 15  0.002747971  0.850059287  0.21351743  1.000000000  0.24060195  0.502344863
## 16  0.241130751  0.218429655  0.90324875  0.240601952  1.00000000  0.119362265
## 17 -0.017473878  0.617792671  0.08320683  0.502344863  0.11936226  1.000000000
## 18 -0.009496380  0.798572055  0.04084227  0.702038262  0.05141598  0.685565464
## 19 -0.040140571  0.198030401  0.46405981  0.199777391  0.44614035  0.294109032
## 20  0.081155540  0.184333691  0.71951971  0.163688027  0.69808255  0.146841262
## 21  0.007779162  0.534245257  0.03177139  0.434825850  0.07579852  0.845142143
## 22  0.026516773  0.719899367  0.04742184  0.632842706  0.06173307  0.598655308
## 23 -0.070052060  0.124663712  0.39857402  0.171427749  0.44647341  0.186038842
## 24  0.076210380  0.173362238  0.62966191  0.170471250  0.65269624  0.070621415
## 25 -0.031668564 -0.012888945 -0.18635587 -0.209601687 -0.15015187  0.217337073
## 26  0.029116254 -0.078789977 -0.18103818 -0.351424691 -0.19393763  0.162767084
## 27 -0.215380942 -0.229566516 -0.31074697 -0.171831940 -0.41839064 -0.069053181
## 28 -0.201974820 -0.059548791 -0.35020001 -0.089888276 -0.44017219 -0.060909315
##              18           19           20           21          22          23
## 1   0.122914043 -0.167543667 -0.087016062 -0.022004238  0.10825797 -0.13094810
## 2   0.220895488 -0.145913504 -0.002383265  0.019281929  0.18356672 -0.20133482
## 3  -0.041744533  0.125386734  0.166348300 -0.122484163 -0.10666437  0.13992502
## 4   0.010539309  0.040622896  0.259048446  0.030615829  0.02107090  0.03255456
## 5   0.170950005 -0.007600010  0.052012833  0.040781104  0.12594352 -0.03068982
## 6   0.230125955 -0.016226872  0.117023536  0.011401361  0.16970594 -0.09628085
## 7   0.050152464  0.082314072  0.179194861 -0.063345918 -0.03788917  0.11985046
## 8   0.064742260  0.071603907  0.253986854  0.036926972  0.07552152  0.04630315
## 9   0.083345915 -0.055474452 -0.034178520  0.007443732  0.04339354 -0.06304134
## 10  0.148992465  0.107163041  0.150081641  0.063947176  0.08974615  0.14149129
## 11  0.008299474 -0.025104914  0.126136088 -0.071355389 -0.05326770 -0.04573669
## 12 -0.009496380 -0.040140571  0.081155540  0.007779162  0.02651677 -0.07005206
## 13  0.798572055  0.198030401  0.184333691  0.534245257  0.71989937  0.12466371
## 14  0.040842268  0.464059805  0.719519714  0.031771395  0.04742184  0.39857402
## 15  0.702038262  0.199777391  0.163688027  0.434825850  0.63284271  0.17142775
## 16  0.051415977  0.446140352  0.698082555  0.075798515  0.06173307  0.44647341
## 17  0.685565464  0.294109032  0.146841262  0.845142143  0.59865531  0.18603884
## 18  1.000000000  0.191139822  0.101363708  0.598718384  0.90741231  0.11654722
## 19  0.191139822  1.000000000  0.679052159  0.232972006  0.18871303  0.85268794
## 20  0.101363708  0.679052159  1.000000000  0.060627800  0.12504491  0.59640413
## 21  0.598718384  0.232972006  0.060627800  1.000000000  0.64613632  0.11090258
## 22  0.907412306  0.188713032  0.125044909  0.646136322  1.00000000  0.10440077
## 23  0.116547220  0.852687936  0.596404134  0.110902582  0.10440077  1.00000000
## 24  0.081930627  0.573398842  0.871146561 -0.004370072  0.09523887  0.64224021
## 25  0.207415810  0.023847487 -0.080780696  0.463568773  0.30547473 -0.06009571
## 26  0.313262504  0.005061934 -0.031440974  0.295632257  0.50249296 -0.06543250
## 27 -0.078896779  0.104504731  0.039055190 -0.085089647 -0.04749002  0.26141426
## 28  0.034537952  0.137964150  0.185264854 -0.097175302  0.03767365  0.21929228
##              24          25           26          27          28
## 1  -0.074204291 -0.05970792  0.045691652 -0.08680434 -0.04811295
## 2  -0.009995103 -0.08492561 -0.016520011 -0.14861005 -0.14405839
## 3   0.146709712 -0.07264656 -0.180409933 -0.22609597 -0.13388354
## 4   0.160703659  0.05517737  0.026475225 -0.35023964 -0.23752323
## 5   0.012409936 -0.05376574 -0.032875983 -0.15761990 -0.11308366
## 6   0.058040588 -0.10260885 -0.092659472 -0.09938359 -0.12663860
## 7   0.202759444 -0.08943299 -0.164057981 -0.15368515 -0.03185161
## 8   0.156591137  0.06799600  0.051670548 -0.40204457 -0.26446270
## 9  -0.058108544 -0.15681501 -0.157206925 -0.08728973 -0.18890087
## 10  0.107646870 -0.13190787 -0.102282144 -0.02545992 -0.12247043
## 11  0.169075753 -0.09342966 -0.087037877 -0.10898785 -0.07474064
## 12  0.076210380 -0.03166856  0.029116254 -0.21538094 -0.20197482
## 13  0.173362238 -0.01288895 -0.078789977 -0.22956652 -0.05954879
## 14  0.629661906 -0.18635587 -0.181038183 -0.31074697 -0.35020001
## 15  0.170471250 -0.20960169 -0.351424691 -0.17183194 -0.08988828
## 16  0.652696236 -0.15015187 -0.193937635 -0.41839064 -0.44017219
## 17  0.070621415  0.21733707  0.162767084 -0.06905318 -0.06090931
## 18  0.081930627  0.20741581  0.313262504 -0.07889678  0.03453795
## 19  0.573398842  0.02384749  0.005061934  0.10450473  0.13796415
## 20  0.871146561 -0.08078070 -0.031440974  0.03905519  0.18526485
## 21 -0.004370072  0.46356877  0.295632257 -0.08508965 -0.09717530
## 22  0.095238865  0.30547473  0.502492962 -0.04749002  0.03767365
## 23  0.642240209 -0.06009571 -0.065432502  0.26141426  0.21929228
## 24  1.000000000 -0.12745736 -0.075144767  0.16684782  0.39297350
## 25 -0.127457356  1.00000000  0.603170923  0.02051880  0.03095518
## 26 -0.075144767  0.60317092  1.000000000  0.13435237  0.14588542
## 27  0.166847817  0.02051880  0.134352369  1.00000000  0.70526942
## 28  0.392973502  0.03095518  0.145885417  0.70526942  1.00000000
## 
## $corrPos
##     xName yName  x  y          corr
## 1       1     1  1 28  1.0000000000
## 2       1     2  1 27  0.4903277676
## 3       1     3  1 26 -0.0296079974
## 4       1     4  1 25 -0.0386324094
## 5       1     5  1 24  0.8754662975
## 6       1     6  1 23  0.4107292830
## 7       1     7  1 22 -0.0121012281
## 8       1     8  1 21 -0.0575759630
## 9       1     9  1 20  0.1689798180
## 10      1    10  1 19  0.0971350406
## 11      1    11  1 18 -0.0326795643
## 12      1    12  1 17 -0.0108420450
## 13      1    13  1 16  0.1672592862
## 14      1    14  1 15 -0.0446503078
## 15      1    15  1 14  0.0765127285
## 16      1    16  1 13 -0.0328313731
## 17      1    17  1 12  0.0664330499
## 18      1    18  1 11  0.1229140434
## 19      1    19  1 10 -0.1675436670
## 20      1    20  1  9 -0.0870160621
## 21      1    21  1  8 -0.0220042375
## 22      1    22  1  7  0.1082579684
## 23      1    23  1  6 -0.1309480953
## 24      1    24  1  5 -0.0742042908
## 25      1    25  1  4 -0.0597079187
## 26      1    26  1  3  0.0456916524
## 27      1    27  1  2 -0.0868043363
## 28      1    28  1  1 -0.0481129550
## 29      2     1  2 28  0.4903277676
## 30      2     2  2 27  1.0000000000
## 31      2     3  2 26  0.0225056320
## 32      2     4  2 25 -0.0324983841
## 33      2     5  2 24  0.4618953067
## 34      2     6  2 23  0.8383800268
## 35      2     7  2 22  0.0771671196
## 36      2     8  2 21 -0.0001852317
## 37      2     9  2 20  0.0968810347
## 38      2    10  2 19  0.2737310777
## 39      2    11  2 18  0.1935325979
## 40      2    12  2 17  0.1628688913
## 41      2    13  2 16  0.2625986004
## 42      2    14  2 15  0.1288951950
## 43      2    15  2 14  0.2135139150
## 44      2    16  2 13  0.1086315041
## 45      2    17  2 12  0.1058151605
## 46      2    18  2 11  0.2208954877
## 47      2    19  2 10 -0.1459135036
## 48      2    20  2  9 -0.0023832646
## 49      2    21  2  8  0.0192819295
## 50      2    22  2  7  0.1835667242
## 51      2    23  2  6 -0.2013348159
## 52      2    24  2  5 -0.0099951034
## 53      2    25  2  4 -0.0849256090
## 54      2    26  2  3 -0.0165200108
## 55      2    27  2  2 -0.1486100483
## 56      2    28  2  1 -0.1440583873
## 57      3     1  3 28 -0.0296079974
## 58      3     2  3 27  0.0225056320
## 59      3     3  3 26  1.0000000000
## 60      3     4  3 25  0.4794484695
## 61      3     5  3 24  0.0755492741
## 62      3     6  3 23  0.0773710112
## 63      3     7  3 22  0.8794367191
## 64      3     8  3 21  0.5418058338
## 65      3     9  3 20  0.0449447792
## 66      3    10  3 19  0.0255677649
## 67      3    11  3 18  0.3534214993
## 68      3    12  3 17  0.1932175628
## 69      3    13  3 16  0.0318543791
## 70      3    14  3 15  0.1615955425
## 71      3    15  3 14  0.0456514844
## 72      3    16  3 13  0.2535071671
## 73      3    17  3 12 -0.0828886224
## 74      3    18  3 11 -0.0417445333
## 75      3    19  3 10  0.1253867341
## 76      3    20  3  9  0.1663482999
## 77      3    21  3  8 -0.1224841629
## 78      3    22  3  7 -0.1066643693
## 79      3    23  3  6  0.1399250193
## 80      3    24  3  5  0.1467097120
## 81      3    25  3  4 -0.0726465577
## 82      3    26  3  3 -0.1804099325
## 83      3    27  3  2 -0.2260959741
## 84      3    28  3  1 -0.1338835355
## 85      4     1  4 28 -0.0386324094
## 86      4     2  4 27 -0.0324983841
## 87      4     3  4 26  0.4794484695
## 88      4     4  4 25  1.0000000000
## 89      4     5  4 24 -0.0705427405
## 90      4     6  4 23 -0.0145432552
## 91      4     7  4 22  0.3667614016
## 92      4     8  4 21  0.8565686170
## 93      4     9  4 20 -0.1216177635
## 94      4    10  4 19  0.0485687281
## 95      4    11  4 18  0.1497357232
## 96      4    12  4 17  0.3309734146
## 97      4    13  4 16  0.1035344685
## 98      4    14  4 15  0.3166804605
## 99      4    15  4 14 -0.0013439609
## 100     4    16  4 13  0.3528525469
## 101     4    17  4 12 -0.0297700728
## 102     4    18  4 11  0.0105393092
## 103     4    19  4 10  0.0406228958
## 104     4    20  4  9  0.2590484460
## 105     4    21  4  8  0.0306158287
## 106     4    22  4  7  0.0210708982
## 107     4    23  4  6  0.0325545574
## 108     4    24  4  5  0.1607036593
## 109     4    25  4  4  0.0551773717
## 110     4    26  4  3  0.0264752249
## 111     4    27  4  2 -0.3502396394
## 112     4    28  4  1 -0.2375232312
## 113     5     1  5 28  0.8754662975
## 114     5     2  5 27  0.4618953067
## 115     5     3  5 26  0.0755492741
## 116     5     4  5 25 -0.0705427405
## 117     5     5  5 24  1.0000000000
## 118     5     6  5 23  0.5335053926
## 119     5     7  5 22  0.1224292904
## 120     5     8  5 21 -0.0355664584
## 121     5     9  5 20  0.3387879444
## 122     5    10  5 19  0.2470884490
## 123     5    11  5 18  0.0974364635
## 124     5    12  5 17 -0.0512346145
## 125     5    13  5 16  0.2243149683
## 126     5    14  5 15  0.0714285982
## 127     5    15  5 14  0.1662140979
## 128     5    16  5 13  0.1052247737
## 129     5    17  5 12  0.1446782248
## 130     5    18  5 11  0.1709500048
## 131     5    19  5 10 -0.0076000101
## 132     5    20  5  9  0.0520128332
## 133     5    21  5  8  0.0407811042
## 134     5    22  5  7  0.1259435209
## 135     5    23  5  6 -0.0306898163
## 136     5    24  5  5  0.0124099362
## 137     5    25  5  4 -0.0537657422
## 138     5    26  5  3 -0.0328759830
## 139     5    27  5  2 -0.1576198997
## 140     5    28  5  1 -0.1130836573
## 141     6     1  6 28  0.4107292830
## 142     6     2  6 27  0.8383800268
## 143     6     3  6 26  0.0773710112
## 144     6     4  6 25 -0.0145432552
## 145     6     5  6 24  0.5335053926
## 146     6     6  6 23  1.0000000000
## 147     6     7  6 22  0.1263809175
## 148     6     8  6 21  0.0560762755
## 149     6     9  6 20  0.3088429632
## 150     6    10  6 19  0.5758382061
## 151     6    11  6 18  0.2026716379
## 152     6    12  6 17  0.1083442845
## 153     6    13  6 16  0.2362318002
## 154     6    14  6 15  0.2084449870
## 155     6    15  6 14  0.2668694997
## 156     6    16  6 13  0.1608474954
## 157     6    17  6 12  0.1111757323
## 158     6    18  6 11  0.2301259552
## 159     6    19  6 10 -0.0162268715
## 160     6    20  6  9  0.1170235359
## 161     6    21  6  8  0.0114013613
## 162     6    22  6  7  0.1697059386
## 163     6    23  6  6 -0.0962808549
## 164     6    24  6  5  0.0580405877
## 165     6    25  6  4 -0.1026088496
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## 627    23    11 23 18 -0.0457366880
## 628    23    12 23 17 -0.0700520604
## 629    23    13 23 16  0.1246637121
## 630    23    14 23 15  0.3985740157
## 631    23    15 23 14  0.1714277491
## 632    23    16 23 13  0.4464734076
## 633    23    17 23 12  0.1860388423
## 634    23    18 23 11  0.1165472199
## 635    23    19 23 10  0.8526879355
## 636    23    20 23  9  0.5964041341
## 637    23    21 23  8  0.1109025815
## 638    23    22 23  7  0.1044007667
## 639    23    23 23  6  1.0000000000
## 640    23    24 23  5  0.6422402089
## 641    23    25 23  4 -0.0600957143
## 642    23    26 23  3 -0.0654325015
## 643    23    27 23  2  0.2614142639
## 644    23    28 23  1  0.2192922794
## 645    24     1 24 28 -0.0742042908
## 646    24     2 24 27 -0.0099951034
## 647    24     3 24 26  0.1467097120
## 648    24     4 24 25  0.1607036593
## 649    24     5 24 24  0.0124099362
## 650    24     6 24 23  0.0580405877
## 651    24     7 24 22  0.2027594443
## 652    24     8 24 21  0.1565911367
## 653    24     9 24 20 -0.0581085444
## 654    24    10 24 19  0.1076468705
## 655    24    11 24 18  0.1690757534
## 656    24    12 24 17  0.0762103797
## 657    24    13 24 16  0.1733622376
## 658    24    14 24 15  0.6296619065
## 659    24    15 24 14  0.1704712503
## 660    24    16 24 13  0.6526962356
## 661    24    17 24 12  0.0706214153
## 662    24    18 24 11  0.0819306268
## 663    24    19 24 10  0.5733988415
## 664    24    20 24  9  0.8711465611
## 665    24    21 24  8 -0.0043700717
## 666    24    22 24  7  0.0952388652
## 667    24    23 24  6  0.6422402089
## 668    24    24 24  5  1.0000000000
## 669    24    25 24  4 -0.1274573557
## 670    24    26 24  3 -0.0751447673
## 671    24    27 24  2  0.1668478166
## 672    24    28 24  1  0.3929735019
## 673    25     1 25 28 -0.0597079187
## 674    25     2 25 27 -0.0849256090
## 675    25     3 25 26 -0.0726465577
## 676    25     4 25 25  0.0551773717
## 677    25     5 25 24 -0.0537657422
## 678    25     6 25 23 -0.1026088496
## 679    25     7 25 22 -0.0894329947
## 680    25     8 25 21  0.0679959988
## 681    25     9 25 20 -0.1568150076
## 682    25    10 25 19 -0.1319078691
## 683    25    11 25 18 -0.0934296646
## 684    25    12 25 17 -0.0316685644
## 685    25    13 25 16 -0.0128889451
## 686    25    14 25 15 -0.1863558704
## 687    25    15 25 14 -0.2096016871
## 688    25    16 25 13 -0.1501518680
## 689    25    17 25 12  0.2173370726
## 690    25    18 25 11  0.2074158099
## 691    25    19 25 10  0.0238474871
## 692    25    20 25  9 -0.0807806963
## 693    25    21 25  8  0.4635687731
## 694    25    22 25  7  0.3054747259
## 695    25    23 25  6 -0.0600957143
## 696    25    24 25  5 -0.1274573557
## 697    25    25 25  4  1.0000000000
## 698    25    26 25  3  0.6031709231
## 699    25    27 25  2  0.0205188033
## 700    25    28 25  1  0.0309551813
## 701    26     1 26 28  0.0456916524
## 702    26     2 26 27 -0.0165200108
## 703    26     3 26 26 -0.1804099325
## 704    26     4 26 25  0.0264752249
## 705    26     5 26 24 -0.0328759830
## 706    26     6 26 23 -0.0926594721
## 707    26     7 26 22 -0.1640579815
## 708    26     8 26 21  0.0516705482
## 709    26     9 26 20 -0.1572069245
## 710    26    10 26 19 -0.1022821440
## 711    26    11 26 18 -0.0870378770
## 712    26    12 26 17  0.0291162544
## 713    26    13 26 16 -0.0787899775
## 714    26    14 26 15 -0.1810381830
## 715    26    15 26 14 -0.3514246911
## 716    26    16 26 13 -0.1939376348
## 717    26    17 26 12  0.1627670836
## 718    26    18 26 11  0.3132625041
## 719    26    19 26 10  0.0050619338
## 720    26    20 26  9 -0.0314409744
## 721    26    21 26  8  0.2956322568
## 722    26    22 26  7  0.5024929624
## 723    26    23 26  6 -0.0654325015
## 724    26    24 26  5 -0.0751447673
## 725    26    25 26  4  0.6031709231
## 726    26    26 26  3  1.0000000000
## 727    26    27 26  2  0.1343523687
## 728    26    28 26  1  0.1458854166
## 729    27     1 27 28 -0.0868043363
## 730    27     2 27 27 -0.1486100483
## 731    27     3 27 26 -0.2260959741
## 732    27     4 27 25 -0.3502396394
## 733    27     5 27 24 -0.1576198997
## 734    27     6 27 23 -0.0993835853
## 735    27     7 27 22 -0.1536851527
## 736    27     8 27 21 -0.4020445744
## 737    27     9 27 20 -0.0872897296
## 738    27    10 27 19 -0.0254599184
## 739    27    11 27 18 -0.1089878520
## 740    27    12 27 17 -0.2153809417
## 741    27    13 27 16 -0.2295665155
## 742    27    14 27 15 -0.3107469703
## 743    27    15 27 14 -0.1718319400
## 744    27    16 27 13 -0.4183906403
## 745    27    17 27 12 -0.0690531808
## 746    27    18 27 11 -0.0788967785
## 747    27    19 27 10  0.1045047315
## 748    27    20 27  9  0.0390551904
## 749    27    21 27  8 -0.0850896473
## 750    27    22 27  7 -0.0474900158
## 751    27    23 27  6  0.2614142639
## 752    27    24 27  5  0.1668478166
## 753    27    25 27  4  0.0205188033
## 754    27    26 27  3  0.1343523687
## 755    27    27 27  2  1.0000000000
## 756    27    28 27  1  0.7052694174
## 757    28     1 28 28 -0.0481129550
## 758    28     2 28 27 -0.1440583873
## 759    28     3 28 26 -0.1338835355
## 760    28     4 28 25 -0.2375232312
## 761    28     5 28 24 -0.1130836573
## 762    28     6 28 23 -0.1266385967
## 763    28     7 28 22 -0.0318516085
## 764    28     8 28 21 -0.2644627015
## 765    28     9 28 20 -0.1889008674
## 766    28    10 28 19 -0.1224704264
## 767    28    11 28 18 -0.0747406430
## 768    28    12 28 17 -0.2019748201
## 769    28    13 28 16 -0.0595487908
## 770    28    14 28 15 -0.3502000079
## 771    28    15 28 14 -0.0898882765
## 772    28    16 28 13 -0.4401721925
## 773    28    17 28 12 -0.0609093146
## 774    28    18 28 11  0.0345379521
## 775    28    19 28 10  0.1379641499
## 776    28    20 28  9  0.1852648538
## 777    28    21 28  8 -0.0971753023
## 778    28    22 28  7  0.0376736495
## 779    28    23 28  6  0.2192922794
## 780    28    24 28  5  0.3929735019
## 781    28    25 28  4  0.0309551813
## 782    28    26 28  3  0.1458854166
## 783    28    27 28  2  0.7052694174
## 784    28    28 28  1  1.0000000000
## 
## $arg
## $arg$type
## [1] "full"

3.2.2 Pairplots

Distribution and plots of data points between two variables for NAcc and Insula pairs.

ggpairs(ahrb_df[,nacc_pairs]) + theme_minimal()

ggpairs(ahrb_df[,insula_pairs]) + theme_minimal()

3.2.3 Bivariate: r > .85

Check if any and which exceed r > .85

# rerun to have original names: 
ahrb_cor = cor(ahrb_df[,mod_vars]) 

# Diagonal are all 1's, convert to 0 to avoid confusion
diag(ahrb_cor) <- 0

# Find indices of correlations exceeding 0.84 on in upper.tri or lower.tri (otherwise redundant)
ahrb_high_index <- which(ahrb_cor > 0.85 | ahrb_cor < -0.85, arr.ind = TRUE)

# Print the correlations that exceed 0.84
ahrbcor_rownames = row.names(ahrb_cor)
ahrbcor_colnames = colnames(ahrb_cor)

# loop through which indices exceed the corr, print value and save name to list
n2_exceed = 0
ahrb_exceedlist = list()
for (i in 1:nrow(ahrb_high_index)) {
  n2_exceed = n2_exceed+1
  row <- ahrb_high_index[i, 1]
  col <- ahrb_high_index[i, 2]
  correlation <- ahrb_cor[row, col]
  print(paste(n2_exceed,"-", ahrbcor_rownames[row], "~", ahrbcor_colnames[col], "r:", round(correlation,3)))
  ahrb_exceedlist[n2_exceed] <- paste(ahrbcor_rownames[row], "~", ahrbcor_colnames[col])
}

## [1] "1 - BWin_v_Neut_L_NAc_r1 ~ AWin_v_Neut_L_NAc_r1 r: 0.875"
## [1] "2 - BWin_v_Neut_L_NAc_r2 ~ AWin_v_Neut_L_NAc_r2 r: 0.879"
## [1] "3 - BWin_v_Neut_R_NAc_r2 ~ AWin_v_Neut_R_NAc_r2 r: 0.857"
## [1] "4 - AWin_v_Neut_L_NAc_r1 ~ BWin_v_Neut_L_NAc_r1 r: 0.875"
## [1] "5 - AWin_v_Neut_L_NAc_r2 ~ BWin_v_Neut_L_NAc_r2 r: 0.879"
## [1] "6 - AWin_v_Neut_R_NAc_r2 ~ BWin_v_Neut_R_NAc_r2 r: 0.857"
## [1] "7 - BWin_v_Neut_R_Ins_r1 ~ AWin_v_Neut_R_Ins_r1 r: 0.85"
## [1] "8 - BWin_v_Neut_R_Ins_r2 ~ AWin_v_Neut_R_Ins_r2 r: 0.903"
## [1] "9 - AWin_v_Neut_R_Ins_r1 ~ BWin_v_Neut_R_Ins_r1 r: 0.85"
## [1] "10 - AWin_v_Neut_R_Ins_r2 ~ BWin_v_Neut_R_Ins_r2 r: 0.903"
## [1] "11 - BLose_v_Neut_R_Ins_r1 ~ ALose_v_Neut_R_Ins_r1 r: 0.907"
## [1] "12 - BLose_v_Neut_L_Ins_r2 ~ ALose_v_Neut_L_Ins_r2 r: 0.853"
## [1] "13 - BLose_v_Neut_R_Ins_r2 ~ ALose_v_Neut_R_Ins_r2 r: 0.871"
## [1] "14 - ALose_v_Neut_R_Ins_r1 ~ BLose_v_Neut_R_Ins_r1 r: 0.907"
## [1] "15 - ALose_v_Neut_L_Ins_r2 ~ BLose_v_Neut_L_Ins_r2 r: 0.853"
## [1] "16 - ALose_v_Neut_R_Ins_r2 ~ BLose_v_Neut_R_Ins_r2 r: 0.871"

# after running, clean environment of uneccessary vars
rm(row,col,correlation,i)

Of the 378 unique correlations, the AHRB study has 16 correlations that are r > .85

3.3 MLS

Run the correlation matrix and plot heatmap. Then, check whether an correlations exceed the Stage 1 specificed > .85

3.3.1 Correlations

Next, just like for ABCD/AHRB, for MLS calculate correlation matrix only for MID model variables (i.e., mod_vars)

# correlation matrix only of the data specified for MID model
mls_cor = cor(mls_df[,mod_vars]) 

# Create table
row.names(mls_cor) <- numstr_modrow_names
colnames(mls_cor) <- numstr_modcol_names
kable(as.data.frame(mls_cor), booktabs = TRUE) %>%
  kable_styling(font_size = 8,position = 'center')

	1_AWin_v_Neut_L_NAc_r1	2_AWin_v_Neut_R_NAc_r1	3_AWin_v_Neut_L_NAc_r2	4_AWin_v_Neut_R_NAc_r2	5_BWin_v_Neut_L_NAc_r1	6_BWin_v_Neut_R_NAc_r1	7_BWin_v_Neut_L_NAc_r2	8_BWin_v_Neut_R_NAc_r2	9_BWin_v_BLose_L_NAc_r1	10_BWin_v_BLose_R_NAc_r1	11_BWin_v_BLose_L_NAc_r2	12_BWin_v_BLose_R_NAc_r2	13_AWin_v_Neut_R_Ins_r1	14_AWin_v_Neut_R_Ins_r2	15_BWin_v_Neut_R_Ins_r1	16_BWin_v_Neut_R_Ins_r2	17_ALose_v_Neut_L_Ins_r1	18_ALose_v_Neut_R_Ins_r1	19_ALose_v_Neut_L_Ins_r2	20_ALose_v_Neut_R_Ins_r2	21_BLose_v_Neut_L_Ins_r1	22_BLose_v_Neut_R_Ins_r1	23_BLose_v_Neut_L_Ins_r2	24_BLose_v_Neut_R_Ins_r2	25_BLose_v_BWin_L_Ins_r1	26_BLose_v_BWin_R_Ins_r1	27_BLose_v_BWin_L_Ins_r2	28_BLose_v_BWin_R_Ins_r2
1_AWin_v_Neut_L_NAc_r1	1.0000000	0.6259024	0.1744192	0.0778583	0.9183982	0.6314682	0.2618212	0.1399196	0.4811439	0.3206389	0.1127402	-0.0126240	-0.0144869	-0.0761232	-0.0384115	0.0014722	0.1247602	0.1162903	0.0382660	0.2192349	0.1116739	0.1122230	-0.0665004	0.1029725	-0.0256736	0.1610086	-0.0856285	0.0932213
2_AWin_v_Neut_R_NAc_r1	0.6259024	1.0000000	0.0949638	0.1380033	0.5831756	0.9091003	0.2075177	0.1986859	0.3355923	0.4771727	0.1634221	0.0938470	-0.0121853	-0.0282163	-0.0265249	0.0072948	0.1117727	0.1088904	0.1282651	0.1137702	0.1123386	0.1391859	0.0239217	0.0540258	-0.0116550	0.1785231	-0.1311725	0.0415653
3_AWin_v_Neut_L_NAc_r2	0.1744192	0.0949638	1.0000000	0.6491610	0.1975329	0.0970497	0.8964749	0.6146682	0.0308387	-0.0853982	0.3259526	0.1641133	0.0583623	0.1511441	0.1510404	0.1864359	0.0381818	0.1614253	0.1086533	0.1821135	0.0280547	0.1949638	0.0360969	0.1594342	0.0680583	0.0625989	-0.2205693	-0.0517133
4_AWin_v_Neut_R_NAc_r2	0.0778583	0.1380033	0.6491610	1.0000000	0.0515802	0.1056219	0.5687959	0.8802706	-0.1019521	-0.1115216	0.0604425	0.1819491	0.1088880	0.1709036	0.1861419	0.2172712	0.1675788	0.1642201	0.0619615	0.1359216	0.1480925	0.2166670	0.0556503	0.1951773	0.0406303	0.0514893	-0.2279835	-0.0516450
5_BWin_v_Neut_L_NAc_r1	0.9183982	0.5831756	0.1975329	0.0515802	1.0000000	0.6905621	0.3022181	0.1150383	0.6383419	0.4387288	0.1245053	-0.0566143	-0.0164835	-0.0637194	-0.0202735	0.0044746	0.1642261	0.1572020	0.0423661	0.2076021	0.1549416	0.1531511	-0.0362106	0.1204357	0.0444703	0.1877346	-0.0647108	0.1062669
6_BWin_v_Neut_R_NAc_r1	0.6314682	0.9091003	0.0970497	0.1056219	0.6905621	1.0000000	0.2219628	0.1749382	0.4650957	0.6461243	0.1594198	0.0654755	-0.0710090	0.0120926	-0.0406375	0.0464779	0.1143437	0.1137889	0.1817276	0.1680629	0.1158511	0.1424560	0.0498620	0.0901248	0.0429567	0.1963709	-0.1639350	0.0334132
7_BWin_v_Neut_L_NAc_r2	0.2618212	0.2075177	0.8964749	0.5687959	0.3022181	0.2219628	1.0000000	0.6698891	0.0981810	0.0186699	0.4632590	0.2627481	0.0866589	0.1814573	0.1615133	0.2204458	0.1188155	0.1994495	0.1737893	0.2397413	0.0945063	0.2308073	0.0888272	0.2022057	0.1033517	0.0914137	-0.2307445	-0.0484876
8_BWin_v_Neut_R_NAc_r2	0.1399196	0.1986859	0.6146682	0.8802706	0.1150383	0.1749382	0.6698891	1.0000000	-0.0760184	-0.0617907	0.1705375	0.3922315	0.0494117	0.2102447	0.1133400	0.2822811	0.1962489	0.1403315	0.1312818	0.2046382	0.1675496	0.1808990	0.0856004	0.2509740	0.0742920	0.0849548	-0.2099191	-0.0693770
9_BWin_v_BLose_L_NAc_r1	0.4811439	0.3355923	0.0308387	-0.1019521	0.6383419	0.4650957	0.0981810	-0.0760184	1.0000000	0.6334566	0.1294944	-0.1253199	-0.0398748	-0.0455780	-0.0136226	0.0063678	0.0360083	0.0737067	0.0681941	0.1182676	-0.0147206	0.0371512	0.0421970	0.0838009	-0.1010775	0.0542689	-0.0731671	0.0708321
10_BWin_v_BLose_R_NAc_r1	0.3206389	0.4771727	-0.0853982	-0.1115216	0.4387288	0.6461243	0.0186699	-0.0617907	0.6334566	1.0000000	0.0644565	0.0068528	-0.0034022	0.0507262	0.0064648	0.0523100	0.0119347	0.0783801	0.1457300	0.1283074	-0.0394478	0.0324793	0.0861540	0.0714053	-0.0570725	0.0289218	-0.0056270	0.0104203
11_BWin_v_BLose_L_NAc_r2	0.1127402	0.1634221	0.3259526	0.0604425	0.1245053	0.1594198	0.4632590	0.1705375	0.1294944	0.0644565	1.0000000	0.5634459	-0.0912295	0.1225857	-0.0230944	0.0655406	-0.0645912	-0.0773353	0.0907324	0.0399282	-0.0656286	-0.0530475	-0.0119552	-0.1296508	-0.0280231	-0.0351418	-0.2469591	-0.1887785
12_BWin_v_BLose_R_NAc_r2	-0.0126240	0.0938470	0.1641133	0.1819491	-0.0566143	0.0654755	0.2627481	0.3922315	-0.1253199	0.0068528	0.5634459	1.0000000	-0.0627364	0.0615143	0.0055483	0.0109126	0.0955113	0.0603333	0.0815978	-0.0225448	0.0812302	0.0617392	-0.0260369	-0.1356181	0.1178549	0.0618947	-0.1136263	-0.1363781
13_AWin_v_Neut_R_Ins_r1	-0.0144869	-0.0121853	0.0583623	0.1088880	-0.0164835	-0.0710090	0.0866589	0.0494117	-0.0398748	-0.0034022	-0.0912295	-0.0627364	1.0000000	0.0833407	0.8709509	0.0939303	0.3798608	0.6327251	0.1276974	0.2058637	0.3450759	0.5474766	0.1623346	0.2088757	-0.0875195	-0.2701080	0.1415777	0.0920017
14_AWin_v_Neut_R_Ins_r2	-0.0761232	-0.0282163	0.1511441	0.1709036	-0.0637194	0.0120926	0.1814573	0.2102447	-0.0455780	0.0507262	0.1225857	0.0615143	0.0833407	1.0000000	0.1230636	0.8722618	0.1100203	0.0669680	0.3644921	0.5624930	0.0899590	0.0307256	0.2989276	0.4544631	0.0582197	-0.0889699	-0.2998943	-0.5083947
15_BWin_v_Neut_R_Ins_r1	-0.0384115	-0.0265249	0.1510404	0.1861419	-0.0202735	-0.0406375	0.1615133	0.1133400	-0.0136226	0.0064648	-0.0230944	0.0055483	0.8709509	0.1230636	1.0000000	0.1461823	0.3883770	0.6342916	0.1879429	0.2731267	0.3511023	0.5455005	0.1557814	0.2749303	-0.1263003	-0.4008848	0.0070976	0.0969873
16_BWin_v_Neut_R_Ins_r2	0.0014722	0.0072948	0.1864359	0.2172712	0.0044746	0.0464779	0.2204458	0.2822811	0.0063678	0.0523100	0.0655406	0.0109126	0.0939303	0.8722618	0.1461823	1.0000000	0.0917691	0.0302031	0.2557896	0.5341030	0.0971457	0.0022412	0.2093803	0.4970349	0.0314183	-0.1432146	-0.3861710	-0.6046348
17_ALose_v_Neut_L_Ins_r1	0.1247602	0.1117727	0.0381818	0.1675788	0.1642261	0.1143437	0.1188155	0.1962489	0.0360083	0.0119347	-0.0645912	0.0955113	0.3798608	0.1100203	0.3883770	0.0917691	1.0000000	0.5898401	0.0328824	0.1266055	0.9124845	0.5473012	0.0574025	0.1702228	0.4755603	0.2109041	0.0051705	0.0585554
18_ALose_v_Neut_R_Ins_r1	0.1162903	0.1088904	0.1614253	0.1642201	0.1572020	0.1137889	0.1994495	0.1403315	0.0737067	0.0783801	-0.0773353	0.0603333	0.6327251	0.0669680	0.6342916	0.0302031	0.5898401	1.0000000	0.0941245	0.1602720	0.5752955	0.8462115	0.0733829	0.2010033	0.3455877	0.2924417	-0.0175190	0.1520485
19_ALose_v_Neut_L_Ins_r2	0.0382660	0.1282651	0.1086533	0.0619615	0.0423661	0.1817276	0.1737893	0.1312818	0.0681941	0.1457300	0.0907324	0.0815978	0.1276974	0.3644921	0.1879429	0.2557896	0.0328824	0.0941245	1.0000000	0.4707989	0.0302432	0.0731729	0.8058670	0.3433699	-0.0839107	-0.1071243	0.0490019	0.0438272
20_ALose_v_Neut_R_Ins_r2	0.2192349	0.1137702	0.1821135	0.1359216	0.2076021	0.1680629	0.2397413	0.2046382	0.1182676	0.1283074	0.0399282	-0.0225448	0.2058637	0.5624930	0.2731267	0.5341030	0.1266055	0.1602720	0.4707989	1.0000000	0.1138236	0.1414385	0.2758383	0.8013361	-0.0055013	-0.1171987	-0.1586433	0.1689302
21_BLose_v_Neut_L_Ins_r1	0.1116739	0.1123386	0.0280547	0.1480925	0.1549416	0.1158511	0.0945063	0.1675496	-0.0147206	-0.0394478	-0.0656286	0.0812302	0.3450759	0.0899590	0.3511023	0.0971457	0.9124845	0.5752955	0.0302432	0.1138236	1.0000000	0.6449479	0.0611417	0.1728205	0.6275308	0.3546932	-0.0077499	0.0551179
22_BLose_v_Neut_R_Ins_r1	0.1122230	0.1391859	0.1949638	0.2166670	0.1531511	0.1424560	0.2308073	0.1808990	0.0371512	0.0324793	-0.0530475	0.0617392	0.5474766	0.0307256	0.5455005	0.0022412	0.5473012	0.8462115	0.0731729	0.1414385	0.6449479	1.0000000	0.0385215	0.1663886	0.4167947	0.5491310	-0.0444685	0.1499808
23_BLose_v_Neut_L_Ins_r2	-0.0665004	0.0239217	0.0360969	0.0556503	-0.0362106	0.0498620	0.0888272	0.0856004	0.0421970	0.0861540	-0.0119552	-0.0260369	0.1623346	0.2989276	0.1557814	0.2093803	0.0574025	0.0733829	0.8058670	0.2758383	0.0611417	0.0385215	1.0000000	0.3806110	0.0135215	-0.1130579	0.2935485	0.1275271
24_BLose_v_Neut_R_Ins_r2	0.1029725	0.0540258	0.1594342	0.1951773	0.1204357	0.0901248	0.2022057	0.2509740	0.0838009	0.0714053	-0.1296508	-0.1356181	0.2088757	0.4544631	0.2749303	0.4970349	0.1702228	0.2010033	0.3433699	0.8013361	0.1728205	0.1663886	0.3806110	1.0000000	0.0616133	-0.0919804	-0.0155894	0.3906214
25_BLose_v_BWin_L_Ins_r1	-0.0256736	-0.0116550	0.0680583	0.0406303	0.0444703	0.0429567	0.1033517	0.0742920	-0.1010775	-0.0570725	-0.0280231	0.1178549	-0.0875195	0.0582197	-0.1263003	0.0314183	0.4755603	0.3455877	-0.0839107	-0.0055013	0.6275308	0.4167947	0.0135215	0.0616133	1.0000000	0.5814965	-0.0139848	0.0227165
26_BLose_v_BWin_R_Ins_r1	0.1610086	0.1785231	0.0625989	0.0514893	0.1877346	0.1963709	0.0914137	0.0849548	0.0542689	0.0289218	-0.0351418	0.0618947	-0.2701080	-0.0889699	-0.4008848	-0.1432146	0.2109041	0.2924417	-0.1071243	-0.1171987	0.3546932	0.5491310	-0.1130579	-0.0919804	0.5814965	1.0000000	-0.0559079	0.0673895
27_BLose_v_BWin_L_Ins_r2	-0.0856285	-0.1311725	-0.2205693	-0.2279835	-0.0647108	-0.1639350	-0.2307445	-0.2099191	-0.0731671	-0.0056270	-0.2469591	-0.1136263	0.1415777	-0.2998943	0.0070976	-0.3861710	0.0051705	-0.0175190	0.0490019	-0.1586433	-0.0077499	-0.0444685	0.2935485	-0.0155894	-0.0139848	-0.0559079	1.0000000	0.3954917
28_BLose_v_BWin_R_Ins_r2	0.0932213	0.0415653	-0.0517133	-0.0516450	0.1062669	0.0334132	-0.0484876	-0.0693770	0.0708321	0.0104203	-0.1887785	-0.1363781	0.0920017	-0.5083947	0.0969873	-0.6046348	0.0585554	0.1520485	0.0438272	0.1689302	0.0551179	0.1499808	0.1275271	0.3906214	0.0227165	0.0673895	0.3954917	1.0000000

# Numeric only for plot
rownames(mls_cor) <- numeric_row
colnames(mls_cor) <- numeric_col

m_cor_plt <- corrplot(mls_cor, method = "color", tl.cex = .6)

m_cor_plt

## $corr
##              1            2           3           4            5           6
## 1   1.00000000  0.625902440  0.17441917  0.07785830  0.918398206  0.63146815
## 2   0.62590244  1.000000000  0.09496375  0.13800331  0.583175637  0.90910035
## 3   0.17441917  0.094963752  1.00000000  0.64916102  0.197532892  0.09704971
## 4   0.07785830  0.138003306  0.64916102  1.00000000  0.051580227  0.10562188
## 5   0.91839821  0.583175637  0.19753289  0.05158023  1.000000000  0.69056208
## 6   0.63146815  0.909100349  0.09704971  0.10562188  0.690562078  1.00000000
## 7   0.26182121  0.207517744  0.89647492  0.56879587  0.302218136  0.22196276
## 8   0.13991960  0.198685901  0.61466820  0.88027056  0.115038335  0.17493817
## 9   0.48114388  0.335592325  0.03083870 -0.10195214  0.638341876  0.46509567
## 10  0.32063892  0.477172698 -0.08539822 -0.11152159  0.438728754  0.64612435
## 11  0.11274019  0.163422071  0.32595263  0.06044249  0.124505342  0.15941980
## 12 -0.01262405  0.093846999  0.16411332  0.18194913 -0.056614302  0.06547545
## 13 -0.01448690 -0.012185251  0.05836225  0.10888805 -0.016483451 -0.07100899
## 14 -0.07612317 -0.028216310  0.15114410  0.17090355 -0.063719352  0.01209263
## 15 -0.03841154 -0.026524920  0.15104041  0.18614188 -0.020273462 -0.04063749
## 16  0.00147222  0.007294843  0.18643595  0.21727120  0.004474626  0.04647785
## 17  0.12476021  0.111772670  0.03818180  0.16757878  0.164226113  0.11434369
## 18  0.11629027  0.108890413  0.16142527  0.16422012  0.157202000  0.11378894
## 19  0.03826597  0.128265107  0.10865333  0.06196152  0.042366146  0.18172755
## 20  0.21923493  0.113770238  0.18211351  0.13592158  0.207602133  0.16806290
## 21  0.11167388  0.112338556  0.02805467  0.14809247  0.154941640  0.11585112
## 22  0.11222301  0.139185896  0.19496376  0.21666699  0.153151071  0.14245602
## 23 -0.06650038  0.023921674  0.03609693  0.05565033 -0.036210617  0.04986201
## 24  0.10297247  0.054025778  0.15943420  0.19517727  0.120435733  0.09012476
## 25 -0.02567362 -0.011654994  0.06805828  0.04063028  0.044470341  0.04295665
## 26  0.16100861  0.178523085  0.06259891  0.05148932  0.187734568  0.19637094
## 27 -0.08562851 -0.131172530 -0.22056928 -0.22798345 -0.064710841 -0.16393496
## 28  0.09322129  0.041565267 -0.05171328 -0.05164501  0.106266884  0.03341322
##              7           8            9           10          11           12
## 1   0.26182121  0.13991960  0.481143883  0.320638919  0.11274019 -0.012624049
## 2   0.20751774  0.19868590  0.335592325  0.477172698  0.16342207  0.093846999
## 3   0.89647492  0.61466820  0.030838703 -0.085398221  0.32595263  0.164113315
## 4   0.56879587  0.88027056 -0.101952140 -0.111521591  0.06044249  0.181949128
## 5   0.30221814  0.11503833  0.638341876  0.438728754  0.12450534 -0.056614302
## 6   0.22196276  0.17493817  0.465095669  0.646124346  0.15941980  0.065475452
## 7   1.00000000  0.66988911  0.098180964  0.018669884  0.46325896  0.262748071
## 8   0.66988911  1.00000000 -0.076018386 -0.061790654  0.17053747  0.392231518
## 9   0.09818096 -0.07601839  1.000000000  0.633456605  0.12949438 -0.125319859
## 10  0.01866988 -0.06179065  0.633456605  1.000000000  0.06445650  0.006852841
## 11  0.46325896  0.17053747  0.129494381  0.064456500  1.00000000  0.563445905
## 12  0.26274807  0.39223152 -0.125319859  0.006852841  0.56344591  1.000000000
## 13  0.08665892  0.04941172 -0.039874761 -0.003402151 -0.09122948 -0.062736402
## 14  0.18145728  0.21024466 -0.045578007  0.050726231  0.12258566  0.061514268
## 15  0.16151329  0.11333997 -0.013622576  0.006464826 -0.02309438  0.005548318
## 16  0.22044578  0.28228113  0.006367822  0.052309994  0.06554056  0.010912573
## 17  0.11881551  0.19624894  0.036008294  0.011934694 -0.06459122  0.095511302
## 18  0.19944948  0.14033147  0.073706711  0.078380126 -0.07733532  0.060333333
## 19  0.17378927  0.13128179  0.068194085  0.145729980  0.09073241  0.081597769
## 20  0.23974133  0.20463818  0.118267552  0.128307427  0.03992823 -0.022544829
## 21  0.09450625  0.16754961 -0.014720622 -0.039447757 -0.06562863  0.081230167
## 22  0.23080733  0.18089902  0.037151184  0.032479253 -0.05304753  0.061739168
## 23  0.08882717  0.08560042  0.042196993  0.086153951 -0.01195521 -0.026036894
## 24  0.20220571  0.25097398  0.083800901  0.071405328 -0.12965085 -0.135618084
## 25  0.10335168  0.07429201 -0.101077549 -0.057072527 -0.02802307  0.117854886
## 26  0.09141368  0.08495477  0.054268897  0.028921811 -0.03514179  0.061894659
## 27 -0.23074446 -0.20991908 -0.073167107 -0.005627022 -0.24695912 -0.113626301
## 28 -0.04848761 -0.06937702  0.070832111  0.010420278 -0.18877845 -0.136378107
##              13          14           15           16           17          18
## 1  -0.014486898 -0.07612317 -0.038411538  0.001472220  0.124760215  0.11629027
## 2  -0.012185251 -0.02821631 -0.026524920  0.007294843  0.111772670  0.10889041
## 3   0.058362252  0.15114410  0.151040409  0.186435948  0.038181802  0.16142527
## 4   0.108888046  0.17090355  0.186141879  0.217271203  0.167578782  0.16422012
## 5  -0.016483451 -0.06371935 -0.020273462  0.004474626  0.164226113  0.15720200
## 6  -0.071008986  0.01209263 -0.040637493  0.046477853  0.114343690  0.11378894
## 7   0.086658916  0.18145728  0.161513289  0.220445777  0.118815512  0.19944948
## 8   0.049411721  0.21024466  0.113339974  0.282281133  0.196248945  0.14033147
## 9  -0.039874761 -0.04557801 -0.013622576  0.006367822  0.036008294  0.07370671
## 10 -0.003402151  0.05072623  0.006464826  0.052309994  0.011934694  0.07838013
## 11 -0.091229485  0.12258566 -0.023094383  0.065540565 -0.064591222 -0.07733532
## 12 -0.062736402  0.06151427  0.005548318  0.010912573  0.095511302  0.06033333
## 13  1.000000000  0.08334073  0.870950922  0.093930314  0.379860824  0.63272515
## 14  0.083340734  1.00000000  0.123063602  0.872261764  0.110020254  0.06696803
## 15  0.870950922  0.12306360  1.000000000  0.146182273  0.388376968  0.63429156
## 16  0.093930314  0.87226176  0.146182273  1.000000000  0.091769085  0.03020305
## 17  0.379860824  0.11002025  0.388376968  0.091769085  1.000000000  0.58984011
## 18  0.632725147  0.06696803  0.634291560  0.030203054  0.589840109  1.00000000
## 19  0.127697413  0.36449206  0.187942891  0.255789586  0.032882408  0.09412446
## 20  0.205863656  0.56249302  0.273126689  0.534103025  0.126605483  0.16027196
## 21  0.345075892  0.08995901  0.351102334  0.097145664  0.912484455  0.57529554
## 22  0.547476622  0.03072560  0.545500543  0.002241213  0.547301250  0.84621146
## 23  0.162334583  0.29892760  0.155781397  0.209380325  0.057402534  0.07338294
## 24  0.208875721  0.45446307  0.274930281  0.497034877  0.170222836  0.20100325
## 25 -0.087519489  0.05821967 -0.126300296  0.031418286  0.475560301  0.34558767
## 26 -0.270107975 -0.08896987 -0.400884824 -0.143214556  0.210904078  0.29244170
## 27  0.141577668 -0.29989434  0.007097633 -0.386170954  0.005170547 -0.01751902
## 28  0.092001688 -0.50839471  0.096987313 -0.604634804  0.058555410  0.15204845
##             19           20           21           22          23          24
## 1   0.03826597  0.219234935  0.111673876  0.112223005 -0.06650038  0.10297247
## 2   0.12826511  0.113770238  0.112338556  0.139185896  0.02392167  0.05402578
## 3   0.10865333  0.182113507  0.028054671  0.194963761  0.03609693  0.15943420
## 4   0.06196152  0.135921585  0.148092472  0.216666988  0.05565033  0.19517727
## 5   0.04236615  0.207602133  0.154941640  0.153151071 -0.03621062  0.12043573
## 6   0.18172755  0.168062897  0.115851123  0.142456017  0.04986201  0.09012476
## 7   0.17378927  0.239741333  0.094506253  0.230807327  0.08882717  0.20220571
## 8   0.13128179  0.204638176  0.167549610  0.180899024  0.08560042  0.25097398
## 9   0.06819408  0.118267552 -0.014720622  0.037151184  0.04219699  0.08380090
## 10  0.14572998  0.128307427 -0.039447757  0.032479253  0.08615395  0.07140533
## 11  0.09073241  0.039928233 -0.065628631 -0.053047529 -0.01195521 -0.12965085
## 12  0.08159777 -0.022544829  0.081230167  0.061739168 -0.02603689 -0.13561808
## 13  0.12769741  0.205863656  0.345075892  0.547476622  0.16233458  0.20887572
## 14  0.36449206  0.562493017  0.089959013  0.030725599  0.29892760  0.45446307
## 15  0.18794289  0.273126689  0.351102334  0.545500543  0.15578140  0.27493028
## 16  0.25578959  0.534103025  0.097145664  0.002241213  0.20938032  0.49703488
## 17  0.03288241  0.126605483  0.912484455  0.547301250  0.05740253  0.17022284
## 18  0.09412446  0.160271963  0.575295539  0.846211460  0.07338294  0.20100325
## 19  1.00000000  0.470798944  0.030243194  0.073172924  0.80586705  0.34336987
## 20  0.47079894  1.000000000  0.113823576  0.141438542  0.27583827  0.80133613
## 21  0.03024319  0.113823576  1.000000000  0.644947873  0.06114172  0.17282046
## 22  0.07317292  0.141438542  0.644947873  1.000000000  0.03852146  0.16638861
## 23  0.80586705  0.275838273  0.061141719  0.038521464  1.00000000  0.38061100
## 24  0.34336987  0.801336127  0.172820459  0.166388611  0.38061100  1.00000000
## 25 -0.08391067 -0.005501309  0.627530778  0.416794723  0.01352148  0.06161326
## 26 -0.10712432 -0.117198653  0.354693169  0.549130965 -0.11305787 -0.09198043
## 27  0.04900192 -0.158643304 -0.007749875 -0.044468548  0.29354848 -0.01558939
## 28  0.04382722  0.168930190  0.055117888  0.149980821  0.12752711  0.39062137
##              25          26           27          28
## 1  -0.025673624  0.16100861 -0.085628506  0.09322129
## 2  -0.011654994  0.17852308 -0.131172530  0.04156527
## 3   0.068058276  0.06259891 -0.220569283 -0.05171328
## 4   0.040630285  0.05148932 -0.227983451 -0.05164501
## 5   0.044470341  0.18773457 -0.064710841  0.10626688
## 6   0.042956655  0.19637094 -0.163934960  0.03341322
## 7   0.103351681  0.09141368 -0.230744458 -0.04848761
## 8   0.074292011  0.08495477 -0.209919082 -0.06937702
## 9  -0.101077549  0.05426890 -0.073167107  0.07083211
## 10 -0.057072527  0.02892181 -0.005627022  0.01042028
## 11 -0.028023070 -0.03514179 -0.246959116 -0.18877845
## 12  0.117854886  0.06189466 -0.113626301 -0.13637811
## 13 -0.087519489 -0.27010798  0.141577668  0.09200169
## 14  0.058219666 -0.08896987 -0.299894338 -0.50839471
## 15 -0.126300296 -0.40088482  0.007097633  0.09698731
## 16  0.031418286 -0.14321456 -0.386170954 -0.60463480
## 17  0.475560301  0.21090408  0.005170547  0.05855541
## 18  0.345587667  0.29244170 -0.017519018  0.15204845
## 19 -0.083910673 -0.10712432  0.049001919  0.04382722
## 20 -0.005501309 -0.11719865 -0.158643304  0.16893019
## 21  0.627530778  0.35469317 -0.007749875  0.05511789
## 22  0.416794723  0.54913096 -0.044468548  0.14998082
## 23  0.013521478 -0.11305787  0.293548477  0.12752711
## 24  0.061613264 -0.09198043 -0.015589388  0.39062137
## 25  1.000000000  0.58149650 -0.013984840  0.02271650
## 26  0.581496497  1.00000000 -0.055907919  0.06738947
## 27 -0.013984840 -0.05590792  1.000000000  0.39549170
## 28  0.022716501  0.06738947  0.395491705  1.00000000
## 
## $corrPos
##     xName yName  x  y         corr
## 1       1     1  1 28  1.000000000
## 2       1     2  1 27  0.625902440
## 3       1     3  1 26  0.174419173
## 4       1     4  1 25  0.077858299
## 5       1     5  1 24  0.918398206
## 6       1     6  1 23  0.631468152
## 7       1     7  1 22  0.261821211
## 8       1     8  1 21  0.139919596
## 9       1     9  1 20  0.481143883
## 10      1    10  1 19  0.320638919
## 11      1    11  1 18  0.112740190
## 12      1    12  1 17 -0.012624049
## 13      1    13  1 16 -0.014486898
## 14      1    14  1 15 -0.076123169
## 15      1    15  1 14 -0.038411538
## 16      1    16  1 13  0.001472220
## 17      1    17  1 12  0.124760215
## 18      1    18  1 11  0.116290266
## 19      1    19  1 10  0.038265973
## 20      1    20  1  9  0.219234935
## 21      1    21  1  8  0.111673876
## 22      1    22  1  7  0.112223005
## 23      1    23  1  6 -0.066500377
## 24      1    24  1  5  0.102972471
## 25      1    25  1  4 -0.025673624
## 26      1    26  1  3  0.161008610
## 27      1    27  1  2 -0.085628506
## 28      1    28  1  1  0.093221285
## 29      2     1  2 28  0.625902440
## 30      2     2  2 27  1.000000000
## 31      2     3  2 26  0.094963752
## 32      2     4  2 25  0.138003306
## 33      2     5  2 24  0.583175637
## 34      2     6  2 23  0.909100349
## 35      2     7  2 22  0.207517744
## 36      2     8  2 21  0.198685901
## 37      2     9  2 20  0.335592325
## 38      2    10  2 19  0.477172698
## 39      2    11  2 18  0.163422071
## 40      2    12  2 17  0.093846999
## 41      2    13  2 16 -0.012185251
## 42      2    14  2 15 -0.028216310
## 43      2    15  2 14 -0.026524920
## 44      2    16  2 13  0.007294843
## 45      2    17  2 12  0.111772670
## 46      2    18  2 11  0.108890413
## 47      2    19  2 10  0.128265107
## 48      2    20  2  9  0.113770238
## 49      2    21  2  8  0.112338556
## 50      2    22  2  7  0.139185896
## 51      2    23  2  6  0.023921674
## 52      2    24  2  5  0.054025778
## 53      2    25  2  4 -0.011654994
## 54      2    26  2  3  0.178523085
## 55      2    27  2  2 -0.131172530
## 56      2    28  2  1  0.041565267
## 57      3     1  3 28  0.174419173
## 58      3     2  3 27  0.094963752
## 59      3     3  3 26  1.000000000
## 60      3     4  3 25  0.649161021
## 61      3     5  3 24  0.197532892
## 62      3     6  3 23  0.097049712
## 63      3     7  3 22  0.896474915
## 64      3     8  3 21  0.614668199
## 65      3     9  3 20  0.030838703
## 66      3    10  3 19 -0.085398221
## 67      3    11  3 18  0.325952630
## 68      3    12  3 17  0.164113315
## 69      3    13  3 16  0.058362252
## 70      3    14  3 15  0.151144099
## 71      3    15  3 14  0.151040409
## 72      3    16  3 13  0.186435948
## 73      3    17  3 12  0.038181802
## 74      3    18  3 11  0.161425275
## 75      3    19  3 10  0.108653327
## 76      3    20  3  9  0.182113507
## 77      3    21  3  8  0.028054671
## 78      3    22  3  7  0.194963761
## 79      3    23  3  6  0.036096926
## 80      3    24  3  5  0.159434204
## 81      3    25  3  4  0.068058276
## 82      3    26  3  3  0.062598908
## 83      3    27  3  2 -0.220569283
## 84      3    28  3  1 -0.051713280
## 85      4     1  4 28  0.077858299
## 86      4     2  4 27  0.138003306
## 87      4     3  4 26  0.649161021
## 88      4     4  4 25  1.000000000
## 89      4     5  4 24  0.051580227
## 90      4     6  4 23  0.105621880
## 91      4     7  4 22  0.568795874
## 92      4     8  4 21  0.880270564
## 93      4     9  4 20 -0.101952140
## 94      4    10  4 19 -0.111521591
## 95      4    11  4 18  0.060442491
## 96      4    12  4 17  0.181949128
## 97      4    13  4 16  0.108888046
## 98      4    14  4 15  0.170903552
## 99      4    15  4 14  0.186141879
## 100     4    16  4 13  0.217271203
## 101     4    17  4 12  0.167578782
## 102     4    18  4 11  0.164220116
## 103     4    19  4 10  0.061961522
## 104     4    20  4  9  0.135921585
## 105     4    21  4  8  0.148092472
## 106     4    22  4  7  0.216666988
## 107     4    23  4  6  0.055650326
## 108     4    24  4  5  0.195177275
## 109     4    25  4  4  0.040630285
## 110     4    26  4  3  0.051489319
## 111     4    27  4  2 -0.227983451
## 112     4    28  4  1 -0.051645010
## 113     5     1  5 28  0.918398206
## 114     5     2  5 27  0.583175637
## 115     5     3  5 26  0.197532892
## 116     5     4  5 25  0.051580227
## 117     5     5  5 24  1.000000000
## 118     5     6  5 23  0.690562078
## 119     5     7  5 22  0.302218136
## 120     5     8  5 21  0.115038335
## 121     5     9  5 20  0.638341876
## 122     5    10  5 19  0.438728754
## 123     5    11  5 18  0.124505342
## 124     5    12  5 17 -0.056614302
## 125     5    13  5 16 -0.016483451
## 126     5    14  5 15 -0.063719352
## 127     5    15  5 14 -0.020273462
## 128     5    16  5 13  0.004474626
## 129     5    17  5 12  0.164226113
## 130     5    18  5 11  0.157202000
## 131     5    19  5 10  0.042366146
## 132     5    20  5  9  0.207602133
## 133     5    21  5  8  0.154941640
## 134     5    22  5  7  0.153151071
## 135     5    23  5  6 -0.036210617
## 136     5    24  5  5  0.120435733
## 137     5    25  5  4  0.044470341
## 138     5    26  5  3  0.187734568
## 139     5    27  5  2 -0.064710841
## 140     5    28  5  1  0.106266884
## 141     6     1  6 28  0.631468152
## 142     6     2  6 27  0.909100349
## 143     6     3  6 26  0.097049712
## 144     6     4  6 25  0.105621880
## 145     6     5  6 24  0.690562078
## 146     6     6  6 23  1.000000000
## 147     6     7  6 22  0.221962765
## 148     6     8  6 21  0.174938174
## 149     6     9  6 20  0.465095669
## 150     6    10  6 19  0.646124346
## 151     6    11  6 18  0.159419803
## 152     6    12  6 17  0.065475452
## 153     6    13  6 16 -0.071008986
## 154     6    14  6 15  0.012092634
## 155     6    15  6 14 -0.040637493
## 156     6    16  6 13  0.046477853
## 157     6    17  6 12  0.114343690
## 158     6    18  6 11  0.113788937
## 159     6    19  6 10  0.181727550
## 160     6    20  6  9  0.168062897
## 161     6    21  6  8  0.115851123
## 162     6    22  6  7  0.142456017
## 163     6    23  6  6  0.049862010
## 164     6    24  6  5  0.090124758
## 165     6    25  6  4  0.042956655
## 166     6    26  6  3  0.196370943
## 167     6    27  6  2 -0.163934960
## 168     6    28  6  1  0.033413218
## 169     7     1  7 28  0.261821211
## 170     7     2  7 27  0.207517744
## 171     7     3  7 26  0.896474915
## 172     7     4  7 25  0.568795874
## 173     7     5  7 24  0.302218136
## 174     7     6  7 23  0.221962765
## 175     7     7  7 22  1.000000000
## 176     7     8  7 21  0.669889106
## 177     7     9  7 20  0.098180964
## 178     7    10  7 19  0.018669884
## 179     7    11  7 18  0.463258962
## 180     7    12  7 17  0.262748071
## 181     7    13  7 16  0.086658916
## 182     7    14  7 15  0.181457277
## 183     7    15  7 14  0.161513289
## 184     7    16  7 13  0.220445777
## 185     7    17  7 12  0.118815512
## 186     7    18  7 11  0.199449476
## 187     7    19  7 10  0.173789274
## 188     7    20  7  9  0.239741333
## 189     7    21  7  8  0.094506253
## 190     7    22  7  7  0.230807327
## 191     7    23  7  6  0.088827168
## 192     7    24  7  5  0.202205707
## 193     7    25  7  4  0.103351681
## 194     7    26  7  3  0.091413681
## 195     7    27  7  2 -0.230744458
## 196     7    28  7  1 -0.048487609
## 197     8     1  8 28  0.139919596
## 198     8     2  8 27  0.198685901
## 199     8     3  8 26  0.614668199
## 200     8     4  8 25  0.880270564
## 201     8     5  8 24  0.115038335
## 202     8     6  8 23  0.174938174
## 203     8     7  8 22  0.669889106
## 204     8     8  8 21  1.000000000
## 205     8     9  8 20 -0.076018386
## 206     8    10  8 19 -0.061790654
## 207     8    11  8 18  0.170537473
## 208     8    12  8 17  0.392231518
## 209     8    13  8 16  0.049411721
## 210     8    14  8 15  0.210244662
## 211     8    15  8 14  0.113339974
## 212     8    16  8 13  0.282281133
## 213     8    17  8 12  0.196248945
## 214     8    18  8 11  0.140331466
## 215     8    19  8 10  0.131281792
## 216     8    20  8  9  0.204638176
## 217     8    21  8  8  0.167549610
## 218     8    22  8  7  0.180899024
## 219     8    23  8  6  0.085600419
## 220     8    24  8  5  0.250973981
## 221     8    25  8  4  0.074292011
## 222     8    26  8  3  0.084954767
## 223     8    27  8  2 -0.209919082
## 224     8    28  8  1 -0.069377022
## 225     9     1  9 28  0.481143883
## 226     9     2  9 27  0.335592325
## 227     9     3  9 26  0.030838703
## 228     9     4  9 25 -0.101952140
## 229     9     5  9 24  0.638341876
## 230     9     6  9 23  0.465095669
## 231     9     7  9 22  0.098180964
## 232     9     8  9 21 -0.076018386
## 233     9     9  9 20  1.000000000
## 234     9    10  9 19  0.633456605
## 235     9    11  9 18  0.129494381
## 236     9    12  9 17 -0.125319859
## 237     9    13  9 16 -0.039874761
## 238     9    14  9 15 -0.045578007
## 239     9    15  9 14 -0.013622576
## 240     9    16  9 13  0.006367822
## 241     9    17  9 12  0.036008294
## 242     9    18  9 11  0.073706711
## 243     9    19  9 10  0.068194085
## 244     9    20  9  9  0.118267552
## 245     9    21  9  8 -0.014720622
## 246     9    22  9  7  0.037151184
## 247     9    23  9  6  0.042196993
## 248     9    24  9  5  0.083800901
## 249     9    25  9  4 -0.101077549
## 250     9    26  9  3  0.054268897
## 251     9    27  9  2 -0.073167107
## 252     9    28  9  1  0.070832111
## 253    10     1 10 28  0.320638919
## 254    10     2 10 27  0.477172698
## 255    10     3 10 26 -0.085398221
## 256    10     4 10 25 -0.111521591
## 257    10     5 10 24  0.438728754
## 258    10     6 10 23  0.646124346
## 259    10     7 10 22  0.018669884
## 260    10     8 10 21 -0.061790654
## 261    10     9 10 20  0.633456605
## 262    10    10 10 19  1.000000000
## 263    10    11 10 18  0.064456500
## 264    10    12 10 17  0.006852841
## 265    10    13 10 16 -0.003402151
## 266    10    14 10 15  0.050726231
## 267    10    15 10 14  0.006464826
## 268    10    16 10 13  0.052309994
## 269    10    17 10 12  0.011934694
## 270    10    18 10 11  0.078380126
## 271    10    19 10 10  0.145729980
## 272    10    20 10  9  0.128307427
## 273    10    21 10  8 -0.039447757
## 274    10    22 10  7  0.032479253
## 275    10    23 10  6  0.086153951
## 276    10    24 10  5  0.071405328
## 277    10    25 10  4 -0.057072527
## 278    10    26 10  3  0.028921811
## 279    10    27 10  2 -0.005627022
## 280    10    28 10  1  0.010420278
## 281    11     1 11 28  0.112740190
## 282    11     2 11 27  0.163422071
## 283    11     3 11 26  0.325952630
## 284    11     4 11 25  0.060442491
## 285    11     5 11 24  0.124505342
## 286    11     6 11 23  0.159419803
## 287    11     7 11 22  0.463258962
## 288    11     8 11 21  0.170537473
## 289    11     9 11 20  0.129494381
## 290    11    10 11 19  0.064456500
## 291    11    11 11 18  1.000000000
## 292    11    12 11 17  0.563445905
## 293    11    13 11 16 -0.091229485
## 294    11    14 11 15  0.122585664
## 295    11    15 11 14 -0.023094383
## 296    11    16 11 13  0.065540565
## 297    11    17 11 12 -0.064591222
## 298    11    18 11 11 -0.077335321
## 299    11    19 11 10  0.090732406
## 300    11    20 11  9  0.039928233
## 301    11    21 11  8 -0.065628631
## 302    11    22 11  7 -0.053047529
## 303    11    23 11  6 -0.011955208
## 304    11    24 11  5 -0.129650849
## 305    11    25 11  4 -0.028023070
## 306    11    26 11  3 -0.035141794
## 307    11    27 11  2 -0.246959116
## 308    11    28 11  1 -0.188778454
## 309    12     1 12 28 -0.012624049
## 310    12     2 12 27  0.093846999
## 311    12     3 12 26  0.164113315
## 312    12     4 12 25  0.181949128
## 313    12     5 12 24 -0.056614302
## 314    12     6 12 23  0.065475452
## 315    12     7 12 22  0.262748071
## 316    12     8 12 21  0.392231518
## 317    12     9 12 20 -0.125319859
## 318    12    10 12 19  0.006852841
## 319    12    11 12 18  0.563445905
## 320    12    12 12 17  1.000000000
## 321    12    13 12 16 -0.062736402
## 322    12    14 12 15  0.061514268
## 323    12    15 12 14  0.005548318
## 324    12    16 12 13  0.010912573
## 325    12    17 12 12  0.095511302
## 326    12    18 12 11  0.060333333
## 327    12    19 12 10  0.081597769
## 328    12    20 12  9 -0.022544829
## 329    12    21 12  8  0.081230167
## 330    12    22 12  7  0.061739168
## 331    12    23 12  6 -0.026036894
## 332    12    24 12  5 -0.135618084
## 333    12    25 12  4  0.117854886
## 334    12    26 12  3  0.061894659
## 335    12    27 12  2 -0.113626301
## 336    12    28 12  1 -0.136378107
## 337    13     1 13 28 -0.014486898
## 338    13     2 13 27 -0.012185251
## 339    13     3 13 26  0.058362252
## 340    13     4 13 25  0.108888046
## 341    13     5 13 24 -0.016483451
## 342    13     6 13 23 -0.071008986
## 343    13     7 13 22  0.086658916
## 344    13     8 13 21  0.049411721
## 345    13     9 13 20 -0.039874761
## 346    13    10 13 19 -0.003402151
## 347    13    11 13 18 -0.091229485
## 348    13    12 13 17 -0.062736402
## 349    13    13 13 16  1.000000000
## 350    13    14 13 15  0.083340734
## 351    13    15 13 14  0.870950922
## 352    13    16 13 13  0.093930314
## 353    13    17 13 12  0.379860824
## 354    13    18 13 11  0.632725147
## 355    13    19 13 10  0.127697413
## 356    13    20 13  9  0.205863656
## 357    13    21 13  8  0.345075892
## 358    13    22 13  7  0.547476622
## 359    13    23 13  6  0.162334583
## 360    13    24 13  5  0.208875721
## 361    13    25 13  4 -0.087519489
## 362    13    26 13  3 -0.270107975
## 363    13    27 13  2  0.141577668
## 364    13    28 13  1  0.092001688
## 365    14     1 14 28 -0.076123169
## 366    14     2 14 27 -0.028216310
## 367    14     3 14 26  0.151144099
## 368    14     4 14 25  0.170903552
## 369    14     5 14 24 -0.063719352
## 370    14     6 14 23  0.012092634
## 371    14     7 14 22  0.181457277
## 372    14     8 14 21  0.210244662
## 373    14     9 14 20 -0.045578007
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## 376    14    12 14 17  0.061514268
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## 378    14    14 14 15  1.000000000
## 379    14    15 14 14  0.123063602
## 380    14    16 14 13  0.872261764
## 381    14    17 14 12  0.110020254
## 382    14    18 14 11  0.066968030
## 383    14    19 14 10  0.364492060
## 384    14    20 14  9  0.562493017
## 385    14    21 14  8  0.089959013
## 386    14    22 14  7  0.030725599
## 387    14    23 14  6  0.298927603
## 388    14    24 14  5  0.454463074
## 389    14    25 14  4  0.058219666
## 390    14    26 14  3 -0.088969866
## 391    14    27 14  2 -0.299894338
## 392    14    28 14  1 -0.508394708
## 393    15     1 15 28 -0.038411538
## 394    15     2 15 27 -0.026524920
## 395    15     3 15 26  0.151040409
## 396    15     4 15 25  0.186141879
## 397    15     5 15 24 -0.020273462
## 398    15     6 15 23 -0.040637493
## 399    15     7 15 22  0.161513289
## 400    15     8 15 21  0.113339974
## 401    15     9 15 20 -0.013622576
## 402    15    10 15 19  0.006464826
## 403    15    11 15 18 -0.023094383
## 404    15    12 15 17  0.005548318
## 405    15    13 15 16  0.870950922
## 406    15    14 15 15  0.123063602
## 407    15    15 15 14  1.000000000
## 408    15    16 15 13  0.146182273
## 409    15    17 15 12  0.388376968
## 410    15    18 15 11  0.634291560
## 411    15    19 15 10  0.187942891
## 412    15    20 15  9  0.273126689
## 413    15    21 15  8  0.351102334
## 414    15    22 15  7  0.545500543
## 415    15    23 15  6  0.155781397
## 416    15    24 15  5  0.274930281
## 417    15    25 15  4 -0.126300296
## 418    15    26 15  3 -0.400884824
## 419    15    27 15  2  0.007097633
## 420    15    28 15  1  0.096987313
## 421    16     1 16 28  0.001472220
## 422    16     2 16 27  0.007294843
## 423    16     3 16 26  0.186435948
## 424    16     4 16 25  0.217271203
## 425    16     5 16 24  0.004474626
## 426    16     6 16 23  0.046477853
## 427    16     7 16 22  0.220445777
## 428    16     8 16 21  0.282281133
## 429    16     9 16 20  0.006367822
## 430    16    10 16 19  0.052309994
## 431    16    11 16 18  0.065540565
## 432    16    12 16 17  0.010912573
## 433    16    13 16 16  0.093930314
## 434    16    14 16 15  0.872261764
## 435    16    15 16 14  0.146182273
## 436    16    16 16 13  1.000000000
## 437    16    17 16 12  0.091769085
## 438    16    18 16 11  0.030203054
## 439    16    19 16 10  0.255789586
## 440    16    20 16  9  0.534103025
## 441    16    21 16  8  0.097145664
## 442    16    22 16  7  0.002241213
## 443    16    23 16  6  0.209380325
## 444    16    24 16  5  0.497034877
## 445    16    25 16  4  0.031418286
## 446    16    26 16  3 -0.143214556
## 447    16    27 16  2 -0.386170954
## 448    16    28 16  1 -0.604634804
## 449    17     1 17 28  0.124760215
## 450    17     2 17 27  0.111772670
## 451    17     3 17 26  0.038181802
## 452    17     4 17 25  0.167578782
## 453    17     5 17 24  0.164226113
## 454    17     6 17 23  0.114343690
## 455    17     7 17 22  0.118815512
## 456    17     8 17 21  0.196248945
## 457    17     9 17 20  0.036008294
## 458    17    10 17 19  0.011934694
## 459    17    11 17 18 -0.064591222
## 460    17    12 17 17  0.095511302
## 461    17    13 17 16  0.379860824
## 462    17    14 17 15  0.110020254
## 463    17    15 17 14  0.388376968
## 464    17    16 17 13  0.091769085
## 465    17    17 17 12  1.000000000
## 466    17    18 17 11  0.589840109
## 467    17    19 17 10  0.032882408
## 468    17    20 17  9  0.126605483
## 469    17    21 17  8  0.912484455
## 470    17    22 17  7  0.547301250
## 471    17    23 17  6  0.057402534
## 472    17    24 17  5  0.170222836
## 473    17    25 17  4  0.475560301
## 474    17    26 17  3  0.210904078
## 475    17    27 17  2  0.005170547
## 476    17    28 17  1  0.058555410
## 477    18     1 18 28  0.116290266
## 478    18     2 18 27  0.108890413
## 479    18     3 18 26  0.161425275
## 480    18     4 18 25  0.164220116
## 481    18     5 18 24  0.157202000
## 482    18     6 18 23  0.113788937
## 483    18     7 18 22  0.199449476
## 484    18     8 18 21  0.140331466
## 485    18     9 18 20  0.073706711
## 486    18    10 18 19  0.078380126
## 487    18    11 18 18 -0.077335321
## 488    18    12 18 17  0.060333333
## 489    18    13 18 16  0.632725147
## 490    18    14 18 15  0.066968030
## 491    18    15 18 14  0.634291560
## 492    18    16 18 13  0.030203054
## 493    18    17 18 12  0.589840109
## 494    18    18 18 11  1.000000000
## 495    18    19 18 10  0.094124459
## 496    18    20 18  9  0.160271963
## 497    18    21 18  8  0.575295539
## 498    18    22 18  7  0.846211460
## 499    18    23 18  6  0.073382944
## 500    18    24 18  5  0.201003253
## 501    18    25 18  4  0.345587667
## 502    18    26 18  3  0.292441701
## 503    18    27 18  2 -0.017519018
## 504    18    28 18  1  0.152048452
## 505    19     1 19 28  0.038265973
## 506    19     2 19 27  0.128265107
## 507    19     3 19 26  0.108653327
## 508    19     4 19 25  0.061961522
## 509    19     5 19 24  0.042366146
## 510    19     6 19 23  0.181727550
## 511    19     7 19 22  0.173789274
## 512    19     8 19 21  0.131281792
## 513    19     9 19 20  0.068194085
## 514    19    10 19 19  0.145729980
## 515    19    11 19 18  0.090732406
## 516    19    12 19 17  0.081597769
## 517    19    13 19 16  0.127697413
## 518    19    14 19 15  0.364492060
## 519    19    15 19 14  0.187942891
## 520    19    16 19 13  0.255789586
## 521    19    17 19 12  0.032882408
## 522    19    18 19 11  0.094124459
## 523    19    19 19 10  1.000000000
## 524    19    20 19  9  0.470798944
## 525    19    21 19  8  0.030243194
## 526    19    22 19  7  0.073172924
## 527    19    23 19  6  0.805867049
## 528    19    24 19  5  0.343369873
## 529    19    25 19  4 -0.083910673
## 530    19    26 19  3 -0.107124321
## 531    19    27 19  2  0.049001919
## 532    19    28 19  1  0.043827218
## 533    20     1 20 28  0.219234935
## 534    20     2 20 27  0.113770238
## 535    20     3 20 26  0.182113507
## 536    20     4 20 25  0.135921585
## 537    20     5 20 24  0.207602133
## 538    20     6 20 23  0.168062897
## 539    20     7 20 22  0.239741333
## 540    20     8 20 21  0.204638176
## 541    20     9 20 20  0.118267552
## 542    20    10 20 19  0.128307427
## 543    20    11 20 18  0.039928233
## 544    20    12 20 17 -0.022544829
## 545    20    13 20 16  0.205863656
## 546    20    14 20 15  0.562493017
## 547    20    15 20 14  0.273126689
## 548    20    16 20 13  0.534103025
## 549    20    17 20 12  0.126605483
## 550    20    18 20 11  0.160271963
## 551    20    19 20 10  0.470798944
## 552    20    20 20  9  1.000000000
## 553    20    21 20  8  0.113823576
## 554    20    22 20  7  0.141438542
## 555    20    23 20  6  0.275838273
## 556    20    24 20  5  0.801336127
## 557    20    25 20  4 -0.005501309
## 558    20    26 20  3 -0.117198653
## 559    20    27 20  2 -0.158643304
## 560    20    28 20  1  0.168930190
## 561    21     1 21 28  0.111673876
## 562    21     2 21 27  0.112338556
## 563    21     3 21 26  0.028054671
## 564    21     4 21 25  0.148092472
## 565    21     5 21 24  0.154941640
## 566    21     6 21 23  0.115851123
## 567    21     7 21 22  0.094506253
## 568    21     8 21 21  0.167549610
## 569    21     9 21 20 -0.014720622
## 570    21    10 21 19 -0.039447757
## 571    21    11 21 18 -0.065628631
## 572    21    12 21 17  0.081230167
## 573    21    13 21 16  0.345075892
## 574    21    14 21 15  0.089959013
## 575    21    15 21 14  0.351102334
## 576    21    16 21 13  0.097145664
## 577    21    17 21 12  0.912484455
## 578    21    18 21 11  0.575295539
## 579    21    19 21 10  0.030243194
## 580    21    20 21  9  0.113823576
## 581    21    21 21  8  1.000000000
## 582    21    22 21  7  0.644947873
## 583    21    23 21  6  0.061141719
## 584    21    24 21  5  0.172820459
## 585    21    25 21  4  0.627530778
## 586    21    26 21  3  0.354693169
## 587    21    27 21  2 -0.007749875
## 588    21    28 21  1  0.055117888
## 589    22     1 22 28  0.112223005
## 590    22     2 22 27  0.139185896
## 591    22     3 22 26  0.194963761
## 592    22     4 22 25  0.216666988
## 593    22     5 22 24  0.153151071
## 594    22     6 22 23  0.142456017
## 595    22     7 22 22  0.230807327
## 596    22     8 22 21  0.180899024
## 597    22     9 22 20  0.037151184
## 598    22    10 22 19  0.032479253
## 599    22    11 22 18 -0.053047529
## 600    22    12 22 17  0.061739168
## 601    22    13 22 16  0.547476622
## 602    22    14 22 15  0.030725599
## 603    22    15 22 14  0.545500543
## 604    22    16 22 13  0.002241213
## 605    22    17 22 12  0.547301250
## 606    22    18 22 11  0.846211460
## 607    22    19 22 10  0.073172924
## 608    22    20 22  9  0.141438542
## 609    22    21 22  8  0.644947873
## 610    22    22 22  7  1.000000000
## 611    22    23 22  6  0.038521464
## 612    22    24 22  5  0.166388611
## 613    22    25 22  4  0.416794723
## 614    22    26 22  3  0.549130965
## 615    22    27 22  2 -0.044468548
## 616    22    28 22  1  0.149980821
## 617    23     1 23 28 -0.066500377
## 618    23     2 23 27  0.023921674
## 619    23     3 23 26  0.036096926
## 620    23     4 23 25  0.055650326
## 621    23     5 23 24 -0.036210617
## 622    23     6 23 23  0.049862010
## 623    23     7 23 22  0.088827168
## 624    23     8 23 21  0.085600419
## 625    23     9 23 20  0.042196993
## 626    23    10 23 19  0.086153951
## 627    23    11 23 18 -0.011955208
## 628    23    12 23 17 -0.026036894
## 629    23    13 23 16  0.162334583
## 630    23    14 23 15  0.298927603
## 631    23    15 23 14  0.155781397
## 632    23    16 23 13  0.209380325
## 633    23    17 23 12  0.057402534
## 634    23    18 23 11  0.073382944
## 635    23    19 23 10  0.805867049
## 636    23    20 23  9  0.275838273
## 637    23    21 23  8  0.061141719
## 638    23    22 23  7  0.038521464
## 639    23    23 23  6  1.000000000
## 640    23    24 23  5  0.380611003
## 641    23    25 23  4  0.013521478
## 642    23    26 23  3 -0.113057874
## 643    23    27 23  2  0.293548477
## 644    23    28 23  1  0.127527108
## 645    24     1 24 28  0.102972471
## 646    24     2 24 27  0.054025778
## 647    24     3 24 26  0.159434204
## 648    24     4 24 25  0.195177275
## 649    24     5 24 24  0.120435733
## 650    24     6 24 23  0.090124758
## 651    24     7 24 22  0.202205707
## 652    24     8 24 21  0.250973981
## 653    24     9 24 20  0.083800901
## 654    24    10 24 19  0.071405328
## 655    24    11 24 18 -0.129650849
## 656    24    12 24 17 -0.135618084
## 657    24    13 24 16  0.208875721
## 658    24    14 24 15  0.454463074
## 659    24    15 24 14  0.274930281
## 660    24    16 24 13  0.497034877
## 661    24    17 24 12  0.170222836
## 662    24    18 24 11  0.201003253
## 663    24    19 24 10  0.343369873
## 664    24    20 24  9  0.801336127
## 665    24    21 24  8  0.172820459
## 666    24    22 24  7  0.166388611
## 667    24    23 24  6  0.380611003
## 668    24    24 24  5  1.000000000
## 669    24    25 24  4  0.061613264
## 670    24    26 24  3 -0.091980425
## 671    24    27 24  2 -0.015589388
## 672    24    28 24  1  0.390621370
## 673    25     1 25 28 -0.025673624
## 674    25     2 25 27 -0.011654994
## 675    25     3 25 26  0.068058276
## 676    25     4 25 25  0.040630285
## 677    25     5 25 24  0.044470341
## 678    25     6 25 23  0.042956655
## 679    25     7 25 22  0.103351681
## 680    25     8 25 21  0.074292011
## 681    25     9 25 20 -0.101077549
## 682    25    10 25 19 -0.057072527
## 683    25    11 25 18 -0.028023070
## 684    25    12 25 17  0.117854886
## 685    25    13 25 16 -0.087519489
## 686    25    14 25 15  0.058219666
## 687    25    15 25 14 -0.126300296
## 688    25    16 25 13  0.031418286
## 689    25    17 25 12  0.475560301
## 690    25    18 25 11  0.345587667
## 691    25    19 25 10 -0.083910673
## 692    25    20 25  9 -0.005501309
## 693    25    21 25  8  0.627530778
## 694    25    22 25  7  0.416794723
## 695    25    23 25  6  0.013521478
## 696    25    24 25  5  0.061613264
## 697    25    25 25  4  1.000000000
## 698    25    26 25  3  0.581496497
## 699    25    27 25  2 -0.013984840
## 700    25    28 25  1  0.022716501
## 701    26     1 26 28  0.161008610
## 702    26     2 26 27  0.178523085
## 703    26     3 26 26  0.062598908
## 704    26     4 26 25  0.051489319
## 705    26     5 26 24  0.187734568
## 706    26     6 26 23  0.196370943
## 707    26     7 26 22  0.091413681
## 708    26     8 26 21  0.084954767
## 709    26     9 26 20  0.054268897
## 710    26    10 26 19  0.028921811
## 711    26    11 26 18 -0.035141794
## 712    26    12 26 17  0.061894659
## 713    26    13 26 16 -0.270107975
## 714    26    14 26 15 -0.088969866
## 715    26    15 26 14 -0.400884824
## 716    26    16 26 13 -0.143214556
## 717    26    17 26 12  0.210904078
## 718    26    18 26 11  0.292441701
## 719    26    19 26 10 -0.107124321
## 720    26    20 26  9 -0.117198653
## 721    26    21 26  8  0.354693169
## 722    26    22 26  7  0.549130965
## 723    26    23 26  6 -0.113057874
## 724    26    24 26  5 -0.091980425
## 725    26    25 26  4  0.581496497
## 726    26    26 26  3  1.000000000
## 727    26    27 26  2 -0.055907919
## 728    26    28 26  1  0.067389475
## 729    27     1 27 28 -0.085628506
## 730    27     2 27 27 -0.131172530
## 731    27     3 27 26 -0.220569283
## 732    27     4 27 25 -0.227983451
## 733    27     5 27 24 -0.064710841
## 734    27     6 27 23 -0.163934960
## 735    27     7 27 22 -0.230744458
## 736    27     8 27 21 -0.209919082
## 737    27     9 27 20 -0.073167107
## 738    27    10 27 19 -0.005627022
## 739    27    11 27 18 -0.246959116
## 740    27    12 27 17 -0.113626301
## 741    27    13 27 16  0.141577668
## 742    27    14 27 15 -0.299894338
## 743    27    15 27 14  0.007097633
## 744    27    16 27 13 -0.386170954
## 745    27    17 27 12  0.005170547
## 746    27    18 27 11 -0.017519018
## 747    27    19 27 10  0.049001919
## 748    27    20 27  9 -0.158643304
## 749    27    21 27  8 -0.007749875
## 750    27    22 27  7 -0.044468548
## 751    27    23 27  6  0.293548477
## 752    27    24 27  5 -0.015589388
## 753    27    25 27  4 -0.013984840
## 754    27    26 27  3 -0.055907919
## 755    27    27 27  2  1.000000000
## 756    27    28 27  1  0.395491705
## 757    28     1 28 28  0.093221285
## 758    28     2 28 27  0.041565267
## 759    28     3 28 26 -0.051713280
## 760    28     4 28 25 -0.051645010
## 761    28     5 28 24  0.106266884
## 762    28     6 28 23  0.033413218
## 763    28     7 28 22 -0.048487609
## 764    28     8 28 21 -0.069377022
## 765    28     9 28 20  0.070832111
## 766    28    10 28 19  0.010420278
## 767    28    11 28 18 -0.188778454
## 768    28    12 28 17 -0.136378107
## 769    28    13 28 16  0.092001688
## 770    28    14 28 15 -0.508394708
## 771    28    15 28 14  0.096987313
## 772    28    16 28 13 -0.604634804
## 773    28    17 28 12  0.058555410
## 774    28    18 28 11  0.152048452
## 775    28    19 28 10  0.043827218
## 776    28    20 28  9  0.168930190
## 777    28    21 28  8  0.055117888
## 778    28    22 28  7  0.149980821
## 779    28    23 28  6  0.127527108
## 780    28    24 28  5  0.390621370
## 781    28    25 28  4  0.022716501
## 782    28    26 28  3  0.067389475
## 783    28    27 28  2  0.395491705
## 784    28    28 28  1  1.000000000
## 
## $arg
## $arg$type
## [1] "full"

3.3.2 Pairplots

Distribution and plots of data points between two variables for NAcc and Insula pairs.

ggpairs(mls_df[,nacc_pairs]) + theme_minimal()

ggpairs(mls_df[,insula_pairs]) + theme_minimal()

3.3.3 Bivariate: r > .85

Check if any and which exceed r > .85

# rerun to have original names: 
mls_cor = cor(mls_df[,mod_vars]) 

# Diagonal are all 1's, convert to 0 to avoid confusion
diag(mls_cor) <- 0

any(mls_cor > 0.85)

## [1] TRUE

# Find indices of correlations exceeding 0.84
mls_high_index <- which(mls_cor > 0.85 | mls_cor < -0.85, arr.ind = TRUE)

# Print the correlations that exceed 0.84
mlscor_rownames = row.names(mls_cor)
mlscor_colnames = colnames(mls_cor)

# loop through which indices exceed the corr, print value and save name to list
n3_exceed = 0
mls_exceedlist = list()
for (i in 1:nrow(mls_high_index)) {
  n3_exceed = n3_exceed+1
  row <- mls_high_index[i, 1]
  col <- mls_high_index[i, 2]
  correlation <- mls_cor[row, col]
  print(paste(n3_exceed,"-", mlscor_rownames[row], "~", mlscor_colnames[col], "r:", round(correlation,3)))
  mls_exceedlist[n3_exceed] <- paste(mlscor_rownames[row], "~", mlscor_colnames[col])
}

## [1] "1 - BWin_v_Neut_L_NAc_r1 ~ AWin_v_Neut_L_NAc_r1 r: 0.918"
## [1] "2 - BWin_v_Neut_R_NAc_r1 ~ AWin_v_Neut_R_NAc_r1 r: 0.909"
## [1] "3 - BWin_v_Neut_L_NAc_r2 ~ AWin_v_Neut_L_NAc_r2 r: 0.896"
## [1] "4 - BWin_v_Neut_R_NAc_r2 ~ AWin_v_Neut_R_NAc_r2 r: 0.88"
## [1] "5 - AWin_v_Neut_L_NAc_r1 ~ BWin_v_Neut_L_NAc_r1 r: 0.918"
## [1] "6 - AWin_v_Neut_R_NAc_r1 ~ BWin_v_Neut_R_NAc_r1 r: 0.909"
## [1] "7 - AWin_v_Neut_L_NAc_r2 ~ BWin_v_Neut_L_NAc_r2 r: 0.896"
## [1] "8 - AWin_v_Neut_R_NAc_r2 ~ BWin_v_Neut_R_NAc_r2 r: 0.88"
## [1] "9 - BWin_v_Neut_R_Ins_r1 ~ AWin_v_Neut_R_Ins_r1 r: 0.871"
## [1] "10 - BWin_v_Neut_R_Ins_r2 ~ AWin_v_Neut_R_Ins_r2 r: 0.872"
## [1] "11 - AWin_v_Neut_R_Ins_r1 ~ BWin_v_Neut_R_Ins_r1 r: 0.871"
## [1] "12 - AWin_v_Neut_R_Ins_r2 ~ BWin_v_Neut_R_Ins_r2 r: 0.872"
## [1] "13 - BLose_v_Neut_L_Ins_r1 ~ ALose_v_Neut_L_Ins_r1 r: 0.912"
## [1] "14 - ALose_v_Neut_L_Ins_r1 ~ BLose_v_Neut_L_Ins_r1 r: 0.912"

# after running, clean environment of uneccessary vars
rm(row,col,correlation,i)

Of the 378 unique correlations, the AHRB study has 14 correlations that are r > .85

3.4 Aggregated Samples

rerun the above but on the combined data. Combining using rbind but emitted some non-matching variables that are unique to ABCD ### Correlation Plot

For MLS/AHRB combined data, calculate correlation matrix for MID model variables (i.e., mod_vars)

# correlation matrix only of the data specified for MID model
brain_comb_corr = cor(brain_set[,mod_vars]) 

# Create table
row.names(brain_comb_corr) <- numstr_modrow_names
colnames(brain_comb_corr) <- numstr_modcol_names
kable(brain_comb_corr, booktabs = TRUE) %>%
  kable_styling(font_size = 8,position = 'center')

	1_AWin_v_Neut_L_NAc_r1	2_AWin_v_Neut_R_NAc_r1	3_AWin_v_Neut_L_NAc_r2	4_AWin_v_Neut_R_NAc_r2	5_BWin_v_Neut_L_NAc_r1	6_BWin_v_Neut_R_NAc_r1	7_BWin_v_Neut_L_NAc_r2	8_BWin_v_Neut_R_NAc_r2	9_BWin_v_BLose_L_NAc_r1	10_BWin_v_BLose_R_NAc_r1	11_BWin_v_BLose_L_NAc_r2	12_BWin_v_BLose_R_NAc_r2	13_AWin_v_Neut_R_Ins_r1	14_AWin_v_Neut_R_Ins_r2	15_BWin_v_Neut_R_Ins_r1	16_BWin_v_Neut_R_Ins_r2	17_ALose_v_Neut_L_Ins_r1	18_ALose_v_Neut_R_Ins_r1	19_ALose_v_Neut_L_Ins_r2	20_ALose_v_Neut_R_Ins_r2	21_BLose_v_Neut_L_Ins_r1	22_BLose_v_Neut_R_Ins_r1	23_BLose_v_Neut_L_Ins_r2	24_BLose_v_Neut_R_Ins_r2	25_BLose_v_BWin_L_Ins_r1	26_BLose_v_BWin_R_Ins_r1	27_BLose_v_BWin_L_Ins_r2	28_BLose_v_BWin_R_Ins_r2
1_AWin_v_Neut_L_NAc_r1	1.0000000	0.6024488	0.1828138	0.1208495	0.8940418	0.5534464	0.1948977	0.1257679	0.3510025	0.2603836	0.0441268	0.0028098	0.1296577	-0.0162160	0.1069217	0.0140538	0.1245206	0.1033728	0.0325999	0.0344330	0.1391690	0.1095878	0.0000392	-0.0016456	-0.0612205	-0.0037998	-0.0412586	-0.0161390
2_AWin_v_Neut_R_NAc_r1	0.6024488	1.0000000	0.1697326	0.1442286	0.5648560	0.8921951	0.1888971	0.1486307	0.2592042	0.4232759	0.0618413	0.0148853	0.1214409	0.0002932	0.1209917	-0.0082795	0.1071157	0.1071849	0.0045975	-0.0070800	0.0976518	0.0944540	-0.0295760	-0.0351124	-0.0895651	-0.0328372	-0.0120395	-0.0295560
3_AWin_v_Neut_L_NAc_r2	0.1828138	0.1697326	1.0000000	0.6352874	0.2329428	0.2092014	0.8927094	0.5753464	0.1246467	0.1044545	0.3278508	0.2124027	-0.0269040	0.2076471	0.0073324	0.1815657	-0.0107613	-0.0329590	0.1024931	0.1152349	-0.0149034	-0.0269224	0.0897193	0.0731132	-0.0019696	-0.0334941	-0.1587946	-0.1069998
4_AWin_v_Neut_R_NAc_r2	0.1208495	0.1442286	0.6352874	1.0000000	0.1252393	0.1468867	0.5599459	0.8851897	0.0654631	0.0680266	0.1635611	0.3050821	-0.0162093	0.2438764	0.0079383	0.2375739	0.0166430	-0.0311975	0.1009420	0.1658738	0.0194711	-0.0203127	0.1312857	0.1490771	-0.0128831	-0.0277506	-0.1040236	-0.0823777
5_BWin_v_Neut_L_NAc_r1	0.8940418	0.5648560	0.2329428	0.1252393	1.0000000	0.6413115	0.2632996	0.1438882	0.5299687	0.3834659	0.0958361	0.0064355	0.1341939	0.0026401	0.1535868	0.0346328	0.1157698	0.0912324	0.0723783	0.0578741	0.1308703	0.0965820	0.0373825	0.0235613	-0.0914622	-0.0639537	-0.0256529	-0.0099119
6_BWin_v_Neut_R_NAc_r1	0.5534464	0.8921951	0.2092014	0.1468867	0.6413115	1.0000000	0.2365046	0.1674309	0.3775798	0.5943972	0.0722887	0.0074051	0.1132895	0.0410743	0.1597234	0.0299763	0.0974080	0.0875031	0.0414725	0.0373636	0.0953653	0.0761569	0.0024951	0.0048711	-0.1065173	-0.0899393	-0.0110935	-0.0254575
7_BWin_v_Neut_L_NAc_r2	0.1948977	0.1888971	0.8927094	0.5599459	0.2632996	0.2365046	1.0000000	0.6290303	0.1545381	0.1455310	0.4919466	0.2992769	-0.0094414	0.1708018	0.0290952	0.1982838	-0.0168810	-0.0312442	0.0909892	0.1132756	-0.0169429	-0.0172508	0.0709011	0.0860096	-0.0333152	-0.0464073	-0.2104891	-0.1102384
8_BWin_v_Neut_R_NAc_r2	0.1257679	0.1486307	0.5753464	0.8851897	0.1438882	0.1674309	0.6290303	1.0000000	0.0893885	0.0970392	0.2696966	0.4894538	-0.0330298	0.1955682	-0.0135376	0.2427134	0.0018389	-0.0492337	0.0908042	0.1224678	0.0108819	-0.0297843	0.1065362	0.1202028	-0.0183300	-0.0148947	-0.1664048	-0.1188678
9_BWin_v_BLose_L_NAc_r1	0.3510025	0.2592042	0.1246467	0.0654631	0.5299687	0.3775798	0.1545381	0.0893885	1.0000000	0.6193315	0.0590297	-0.0132314	0.0971158	0.0007454	0.1597016	0.0282952	-0.0530296	-0.0443434	0.0367616	0.0293328	-0.0712245	-0.0801776	0.0440703	0.0281751	-0.2618438	-0.2403789	0.0189068	0.0015071
10_BWin_v_BLose_R_NAc_r1	0.2603836	0.4232759	0.1044545	0.0680266	0.3834659	0.5943972	0.1455310	0.0970392	0.6193315	1.0000000	0.0701168	0.0137952	0.0929415	0.0247823	0.1550773	0.0281441	0.0269474	-0.0018834	0.0293031	0.0400146	-0.0075233	-0.0409956	0.0296578	0.0298370	-0.2113154	-0.1980809	0.0404027	0.0034193
11_BWin_v_BLose_L_NAc_r2	0.0441268	0.0618413	0.3278508	0.1635611	0.0958361	0.0722887	0.4919466	0.2696966	0.0590297	0.0701168	1.0000000	0.5646156	-0.0894004	0.0105686	-0.0826619	0.0558709	-0.0906491	-0.0987665	-0.0771350	-0.0981353	-0.0920922	-0.0697389	-0.1366352	-0.1320746	-0.0336177	0.0173224	-0.2671214	-0.2002658
12_BWin_v_BLose_R_NAc_r2	0.0028098	0.0148853	0.2124027	0.3050821	0.0064355	0.0074051	0.2992769	0.4894538	-0.0132314	0.0137952	0.5646156	1.0000000	-0.1226426	-0.0060299	-0.1036122	0.0378164	-0.0510204	-0.1039094	-0.1050366	-0.1381971	-0.0473610	-0.0667769	-0.1556170	-0.1678177	0.0162996	0.0415427	-0.2488915	-0.2204105
13_AWin_v_Neut_R_Ins_r1	0.1296577	0.1214409	-0.0269040	-0.0162093	0.1341939	0.1132895	-0.0094414	-0.0330298	0.0971158	0.0929415	-0.0894004	-0.1226426	1.0000000	0.1026013	0.8749466	0.0646819	0.4299471	0.6464031	0.1779722	0.1535210	0.3912039	0.5445109	0.1748091	0.1517765	-0.1883098	-0.3700185	0.0912048	0.0978334
14_AWin_v_Neut_R_Ins_r2	-0.0162160	0.0002932	0.2076471	0.2438764	0.0026401	0.0410743	0.1708018	0.1955682	0.0007454	0.0247823	0.0105686	-0.0060299	0.1026013	1.0000000	0.1305121	0.8742537	0.1026853	0.0907848	0.4185861	0.6698371	0.0866276	0.0862404	0.3902270	0.5605544	-0.0120843	-0.0503294	-0.1656994	-0.2899834
15_BWin_v_Neut_R_Ins_r1	0.1069217	0.1209917	0.0073324	0.0079383	0.1535868	0.1597234	0.0290952	-0.0135376	0.1597016	0.1550773	-0.0826619	-0.1036122	0.8749466	0.1305121	1.0000000	0.0906419	0.4071614	0.5903788	0.1933597	0.1809014	0.3643521	0.4938655	0.1858845	0.1783129	-0.2986660	-0.5465943	0.0702468	0.0998127
16_BWin_v_Neut_R_Ins_r2	0.0140538	-0.0082795	0.1815657	0.2375739	0.0346328	0.0299763	0.1982838	0.2427134	0.0282952	0.0281441	0.0558709	0.0378164	0.0646819	0.8742537	0.0906419	1.0000000	0.0586036	0.0462731	0.3766728	0.6286709	0.0544483	0.0497867	0.3595652	0.5506160	0.0037571	-0.0446805	-0.2855040	-0.4296190
17_ALose_v_Neut_L_Ins_r1	0.1245206	0.1071157	-0.0107613	0.0166430	0.1157698	0.0974080	-0.0168810	0.0018389	-0.0530296	0.0269474	-0.0906491	-0.0510204	0.4299471	0.1026853	0.4071614	0.0586036	1.0000000	0.6173548	0.1338783	0.1035909	0.8915031	0.5486947	0.0943638	0.0630118	0.2916797	0.1122076	-0.0044349	0.0081848
18_ALose_v_Neut_R_Ins_r1	0.1033728	0.1071849	-0.0329590	-0.0311975	0.0912324	0.0875031	-0.0312442	-0.0492337	-0.0443434	-0.0018834	-0.0987665	-0.1039094	0.6464031	0.0907848	0.5903788	0.0462731	0.6173548	1.0000000	0.1519196	0.1213958	0.5614680	0.8626144	0.1413671	0.1144321	0.2329031	0.2272292	0.0436015	0.0763034
19_ALose_v_Neut_L_Ins_r2	0.0325999	0.0045975	0.1024931	0.1009420	0.0723783	0.0414725	0.0909892	0.0908042	0.0367616	0.0293031	-0.0771350	-0.1050366	0.1779722	0.4185861	0.1933597	0.3766728	0.1338783	0.1519196	1.0000000	0.6731888	0.1153147	0.1187957	0.8546807	0.5748462	-0.0755396	-0.0831851	0.2725446	0.2357516
20_ALose_v_Neut_R_Ins_r2	0.0344330	-0.0070800	0.1152349	0.1658738	0.0578741	0.0373636	0.1132756	0.1224678	0.0293328	0.0400146	-0.0981353	-0.1381971	0.1535210	0.6698371	0.1809014	0.6286709	0.1035909	0.1213958	0.6731888	1.0000000	0.1060770	0.1287378	0.5937452	0.8664396	-0.0460815	-0.0608617	0.1783054	0.2927206
21_BLose_v_Neut_L_Ins_r1	0.1391690	0.0976518	-0.0149034	0.0194711	0.1308703	0.0953653	-0.0169429	0.0108819	-0.0712245	-0.0075233	-0.0920922	-0.0473610	0.3912039	0.0866276	0.3643521	0.0544483	0.8915031	0.5614680	0.1153147	0.1060770	1.0000000	0.6354982	0.0698127	0.0738932	0.4710248	0.2395068	-0.0125000	0.0240957
22_BLose_v_Neut_R_Ins_r1	0.1095878	0.0944540	-0.0269224	-0.0203127	0.0965820	0.0761569	-0.0172508	-0.0297843	-0.0801776	-0.0409956	-0.0697389	-0.0667769	0.5445109	0.0862404	0.4938655	0.0497867	0.5486947	0.8626144	0.1187957	0.1287378	0.6354982	1.0000000	0.0982517	0.1213465	0.3491351	0.4582021	0.0092922	0.0801869
23_BLose_v_Neut_L_Ins_r2	0.0000392	-0.0295760	0.0897193	0.1312857	0.0373825	0.0024951	0.0709011	0.1065362	0.0440703	0.0296578	-0.1366352	-0.1556170	0.1748091	0.3902270	0.1858845	0.3595652	0.0943638	0.1413671	0.8546807	0.5937452	0.0698127	0.0982517	1.0000000	0.6768919	-0.0912201	-0.0954228	0.4574906	0.3637477
24_BLose_v_Neut_R_Ins_r2	-0.0016456	-0.0351124	0.0731132	0.1490771	0.0235613	0.0048711	0.0860096	0.1202028	0.0281751	0.0298370	-0.1320746	-0.1678177	0.1517765	0.5605544	0.1783129	0.5506160	0.0630118	0.1144321	0.5748462	0.8664396	0.0738932	0.1213465	0.6768919	1.0000000	-0.0454141	-0.0654460	0.2969921	0.5172375
25_BLose_v_BWin_L_Ins_r1	-0.0612205	-0.0895651	-0.0019696	-0.0128831	-0.0914622	-0.1065173	-0.0333152	-0.0183300	-0.2618438	-0.2113154	-0.0336177	0.0162996	-0.1883098	-0.0120843	-0.2986660	0.0037571	0.2916797	0.2329031	-0.0755396	-0.0460815	0.4710248	0.3491351	-0.0912201	-0.0454141	1.0000000	0.6415190	-0.0740315	-0.0530710
26_BLose_v_BWin_R_Ins_r1	-0.0037998	-0.0328372	-0.0334941	-0.0277506	-0.0639537	-0.0899393	-0.0464073	-0.0148947	-0.2403789	-0.1980809	0.0173224	0.0415427	-0.3700185	-0.0503294	-0.5465943	-0.0446805	0.1122076	0.2272292	-0.0831851	-0.0608617	0.2395068	0.4582021	-0.0954228	-0.0654460	0.6415190	1.0000000	-0.0630006	-0.0248722
27_BLose_v_BWin_L_Ins_r2	-0.0412586	-0.0120395	-0.1587946	-0.1040236	-0.0256529	-0.0110935	-0.2104891	-0.1664048	0.0189068	0.0404027	-0.2671214	-0.2488915	0.0912048	-0.1656994	0.0702468	-0.2855040	-0.0044349	0.0436015	0.2725446	0.1783054	-0.0125000	0.0092922	0.4574906	0.2969921	-0.0740315	-0.0630006	1.0000000	0.6140180
28_BLose_v_BWin_R_Ins_r2	-0.0161390	-0.0295560	-0.1069998	-0.0823777	-0.0099119	-0.0254575	-0.1102384	-0.1188678	0.0015071	0.0034193	-0.2002658	-0.2204105	0.0978334	-0.2899834	0.0998127	-0.4296190	0.0081848	0.0763034	0.2357516	0.2927206	0.0240957	0.0801869	0.3637477	0.5172375	-0.0530710	-0.0248722	0.6140180	1.0000000

# numeric
rownames(brain_comb_corr) <- numeric_row
colnames(brain_comb_corr) <- numeric_col

corrplot(brain_comb_corr, method = "color", tl.cex = .6, diag = TRUE)

3.4.1 Intersection corrs exceed/below

Below, we aggregate the correlations that => .85 acros the samples.

exceed_intersect = intersect(abcd_exceedlist, ahrb_exceedlist)
exceed_intersect = intersect(mls_exceedlist,exceed_intersect)

cat(paste(length(exceed_intersect), "items exceed r .85 in ABCD, AHRB and MLS, they are: ", paste(exceed_intersect, collapse = ", ")))

## 10 items exceed r .85 in ABCD, AHRB and MLS, they are:  BWin_v_Neut_L_NAc_r1 ~ AWin_v_Neut_L_NAc_r1, BWin_v_Neut_L_NAc_r2 ~ AWin_v_Neut_L_NAc_r2, BWin_v_Neut_R_NAc_r2 ~ AWin_v_Neut_R_NAc_r2, AWin_v_Neut_L_NAc_r1 ~ BWin_v_Neut_L_NAc_r1, AWin_v_Neut_L_NAc_r2 ~ BWin_v_Neut_L_NAc_r2, AWin_v_Neut_R_NAc_r2 ~ BWin_v_Neut_R_NAc_r2, BWin_v_Neut_R_Ins_r1 ~ AWin_v_Neut_R_Ins_r1, BWin_v_Neut_R_Ins_r2 ~ AWin_v_Neut_R_Ins_r2, AWin_v_Neut_R_Ins_r1 ~ BWin_v_Neut_R_Ins_r1, AWin_v_Neut_R_Ins_r2 ~ BWin_v_Neut_R_Ins_r2

4 CFA Analyses

In this section, the CFA and Multigroup CFA analyses are performed. The registered report used simulated data. Below, cfa() is fit to data using the aprior model. The fit statistics are extracted to describe how the population model fits the empirical data.

4.1 Specify MID CFA Model

Per the correlations that exceed .85, BWin_v_Neut_L_NAc_r1 ~ AWin_v_Neut_L_NAc_r1, BWin_v_Neut_L_NAc_r2 ~ AWin_v_Neut_L_NAc_r2, BWin_v_Neut_R_NAc_r2 ~ AWin_v_Neut_R_NAc_r2, AWin_v_Neut_L_NAc_r1 ~ BWin_v_Neut_L_NAc_r1, AWin_v_Neut_L_NAc_r2 ~ BWin_v_Neut_L_NAc_r2, AWin_v_Neut_R_NAc_r2 ~ BWin_v_Neut_R_NAc_r2, BWin_v_Neut_R_Ins_r1 ~ AWin_v_Neut_R_Ins_r1, BWin_v_Neut_R_Ins_r2 ~ AWin_v_Neut_R_Ins_r2, AWin_v_Neut_R_Ins_r1 ~ BWin_v_Neut_R_Ins_r1, AWin_v_Neut_R_Ins_r2 ~ BWin_v_Neut_R_Ins_r2

The following parameters are fixed (pre-multiplied, as example given here) in the pre-specified population [theoretical] model:

• AWin_v_Neut_L_NAc_r1 ~ BWin_v_Neut_L_NAc_r1 (a)
• BWin_v_Neut_L_NAc_r2 ~ AWin_v_Neut_L_NAc_r2 (b)
• BWin_v_Neut_R_Ins_r1 ~ AWin_v_Neut_R_Ins_r1 (c)
• BWin_v_Neut_R_Ins_r2 ~ AWin_v_Neut_R_Ins_r2 (d)
• AWin_v_Neut_R_NAc_r2 ~ BWin_v_Neut_R_NAc_r2 (e)

mid_model <-"
# Factor loadings
Approach =~ BWin_v_BLose_L_NAc_r1 + BWin_v_BLose_R_NAc_r1 +
            a*AWin_v_Neut_L_NAc_r1  + AWin_v_Neut_R_NAc_r1  + c*AWin_v_Neut_R_Ins_r1 +
            a*BWin_v_Neut_L_NAc_r1  + BWin_v_Neut_R_NAc_r1  + c*BWin_v_Neut_R_Ins_r1 +
            b*AWin_v_Neut_L_NAc_r2  + e*AWin_v_Neut_R_NAc_r2  + d*AWin_v_Neut_R_Ins_r2 +
            b*BWin_v_Neut_L_NAc_r2  + e*BWin_v_Neut_R_NAc_r2  + d*BWin_v_Neut_R_Ins_r2 +
            BWin_v_BLose_L_NAc_r2 + BWin_v_BLose_R_NAc_r2 
                
Avoid =~    BLose_v_Neut_L_Ins_r1 + BLose_v_Neut_R_Ins_r1 +
            BLose_v_BWin_L_Ins_r1 + BLose_v_BWin_R_Ins_r1 +
            ALose_v_Neut_L_Ins_r2 + ALose_v_Neut_R_Ins_r2 +
            BLose_v_Neut_L_Ins_r2 + BLose_v_Neut_R_Ins_r2 +
            ALose_v_Neut_L_Ins_r1 + ALose_v_Neut_R_Ins_r1 +
            BLose_v_BWin_L_Ins_r2 + BLose_v_BWin_R_Ins_r2 

# covariance between factors   
Approach ~~ Avoid
"

4.2 Strict CFA

Below is the CFA model that is used to test the proposed restricted model (see Figure 1 in the manuscript). The CFA fitting procedure is consistent with the description here. A CFA model is estimated for the complete data (i.e., all three datasets). The std.lv= = FALSE constrains the latent factor variances to 1. The estimator being used is ML, maximum-likelihood estimator.

Below, the proposed strict model is ran on the combined samples. In other words, all of the data are combined and a CFA model is fit assuming all structure, loadings and vairances are equal.

all_sample <- cfa(model = mid_model, data = brain_set,
               estimator = "ML", std.lv = FALSE, meanstructure = TRUE)

4.3 Configural MG-CFA

Here, the configular multigroup model is fit. As described in D’Urso et al. (2022) In measurement invariance, the configural model tests:

is the structure of the factors invariant across the samples (data sets). In other words, if an a priori two-factor structure is assumed (FA 1 = approach and FA 2 = Avoidance), is this two factor structure which represents the between-person variability in the items reflecting the factors consistent across the samples?

If the variability in one sample suggests a one, three, or four factor structure, this will be degrade the fit statistics. A pre-specified CFA model is used to evaluate whether the manifest variables that reflect the factor are the same across groups. This is less restrictive than the strict CFA model, as it only imposed structural constraints.

configural_cfa <- cfa(model = mid_model, data = brain_set, group = 'set', 
                      estimator = "ML", std.lv = FALSE, meanstructure = TRUE)

4.4 Metric MG-CFA

After fitting the CFA configurial (factor structure) invariance, if the model fit is not poor, then the next step is to test the metric invariance. [Given the configural model has poor fit, this is only fit here for reporting but not interpretation purposes as the model will inevitabily be poor fit].

Metric invariance tests:

are the loadings consistent across the groups. In other words, are the phenomena (i.e., approach and avoidance) reflected by the same pattern of item loadings?

One cause for concern may be that the phenomenon are not invariant across age groups. Or, the items/measures (ROIs for a given contrast) do not load in the same manner onto each factor. This ‘soft’ measure of invariance can determine whether the items function differently across the samples and so cannot be easily compared.

The model is fit using the same procedure as for configurial invariance with one exception: In metric invariance the loadings group equality constraint is added to the model via group.equal=c("loadings").

metric_cfa <-cfa(model = mid_model, data = brain_set, 
                 group = 'set', group.equal=c("loadings"),
                 estimator = "ML", std.lv = FALSE, meanstructure = TRUE)

4.5 Extract Fit CFA

Fit statistics are extracted out and saved into the out data frame:

• Model Name,
• Chi-square statistics,
• Model Degrees of Freedom (df),
• Model p-value,
• RMSEA,
• CFI,
• SRMR,
• AIC,
• BIC

# Below selects specific fit data as described in Maassen et al. 2019 OSF. No comparisons are made to compare models at this point.
out <- matrix(NA, ncol = 10, nrow = 4)
colnames(out) <- c(" ","χ2","DF","p-value", "RMSEA", "SRMR", "TLI","CFI", "AIC", "BIC")
# save fit measures from models
out[1,2:8] <- round(data.matrix(
  fitmeasures(all_sample, fit.measures = c("chisq","df","pvalue","rmsea", "srmr", "tli", "cfi"))), digits=2)
out[2,2:8] <- round(data.matrix(
  fitmeasures(configural_cfa, fit.measures = c("chisq","df","pvalue","rmsea", "srmr", "tli", "cfi"))),  digits=2)
out[3,2:8] <- round(data.matrix(
  fitmeasures(metric_cfa,fit.measures = c("chisq","df","pvalue","rmsea", "srmr", "tli", "cfi"))), digits=2)

# AIC models
out[1,9] <- round(AIC(all_sample),0)
out[2,9] <- round(AIC(configural_cfa),0)
out[3,9] <- round(AIC(metric_cfa),0)
# BIC models
out[1,10] <- round(BIC(all_sample),0)
out[2,10] <- round(BIC(configural_cfa),0)
out[3,10] <- round(BIC(metric_cfa),0)
out[1:3,1] <-  c("Overall CFA", "Configg MG-CFA", "Metric MG-CFA")

4.5.1 Summary: Model Parameters

Reporting standardized coefficients for three models:

• Strict [combined data] Model
• Configural Model: Structure constraint across groups (samples)
• Metric Model: structure + loadings constraint across groups (samples)

4.5.1.1 Strict CFA Model

##### Summarizing All Samples CFA model #####
#parameters(all_sample, standardize = T)
allsample_params = data.frame(parameters(all_sample, standardize = T)) %>% 
  slice(1:29) %>% 
  select(-c("z","Component","CI_low","CI_high")) %>% 
  rename("Fixed" = Label, "β" = Coefficient)

allsample_params$p <- if_else(allsample_params$p < .001, "< .001", 
                           if_else(allsample_params$p < .01, "< .01", 
                                   if_else(allsample_params$p < .05, "< .05", "> .05")))
allsample_params[,4:5] <- round(allsample_params[,c(4:5)],2)

# Report table
kable(allsample_params, booktabs = TRUE) %>%
  kable_styling(font_size = 12, position = 'center',html_font = "Times New Roman")

To	Operator	From	β	SE	p	Fixed
Approach	=~	BWin_v_BLose_L_NAc_r1	0.50	0.03	< .001
Approach	=~	BWin_v_BLose_R_NAc_r1	0.46	0.04	< .001
Approach	=~	AWin_v_Neut_L_NAc_r1	0.90	0.01	< .001	a
Approach	=~	AWin_v_Neut_R_NAc_r1	0.71	0.02	< .001
Approach	=~	AWin_v_Neut_R_Ins_r1	0.18	0.03	< .001	c
Approach	=~	BWin_v_Neut_L_NAc_r1	0.90	0.01	< .001	a
Approach	=~	BWin_v_Neut_R_NAc_r1	0.74	0.02	< .001
Approach	=~	BWin_v_Neut_R_Ins_r1	0.15	0.03	< .001	c
Approach	=~	AWin_v_Neut_L_NAc_r2	0.32	0.03	< .001	b
Approach	=~	AWin_v_Neut_R_NAc_r2	0.22	0.03	< .001	e
Approach	=~	AWin_v_Neut_R_Ins_r2	0.04	0.03	> .05	d
Approach	=~	BWin_v_Neut_L_NAc_r2	0.27	0.03	< .001	b
Approach	=~	BWin_v_Neut_R_NAc_r2	0.19	0.03	< .001	e
Approach	=~	BWin_v_Neut_R_Ins_r2	0.04	0.03	> .05	d
Approach	=~	BWin_v_BLose_L_NAc_r2	0.11	0.04	< .05
Approach	=~	BWin_v_BLose_R_NAc_r2	0.04	0.04	> .05
Avoid	=~	BLose_v_Neut_L_Ins_r1	0.96	0.01	< .001
Avoid	=~	BLose_v_Neut_R_Ins_r1	0.68	0.02	< .001
Avoid	=~	BLose_v_BWin_L_Ins_r1	0.44	0.04	< .001
Avoid	=~	BLose_v_BWin_R_Ins_r1	0.25	0.04	< .001
Avoid	=~	ALose_v_Neut_L_Ins_r2	0.14	0.04	< .01
Avoid	=~	ALose_v_Neut_R_Ins_r2	0.13	0.04	< .01
Avoid	=~	BLose_v_Neut_L_Ins_r2	0.10	0.04	< .05
Avoid	=~	BLose_v_Neut_R_Ins_r2	0.09	0.04	< .05
Avoid	=~	ALose_v_Neut_L_Ins_r1	0.91	0.01	< .001
Avoid	=~	ALose_v_Neut_R_Ins_r1	0.64	0.03	< .001
Avoid	=~	BLose_v_BWin_L_Ins_r2	0.00	0.04	> .05
Avoid	=~	BLose_v_BWin_R_Ins_r2	0.03	0.04	> .05
Approach	~~	Avoid	0.14	0.04	< .01

4.5.1.2 Configural CFA Model

##### Summarizing Configural MG-CFA model #####
parameters(configural_cfa, standardize = T)

## # Loading
## 
## Link                                 | Coefficient |   SE |        95% CI |     z |      p | Group
## --------------------------------------------------------------------------------------------------
## Approach =~ BWin_v_BLose_L_NAc_r1    |        0.38 | 0.04 | [ 0.31, 0.45] | 10.63 | < .001 |  1.00
## Approach =~ BWin_v_BLose_R_NAc_r1    |        0.57 | 0.04 | [ 0.49, 0.64] | 14.95 | < .001 |  1.00
## Approach =~ AWin_v_Neut_L_NAc_r1 (a) |        0.69 | 0.03 | [ 0.63, 0.74] | 26.71 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_NAc_r1     |        0.92 | 0.01 | [ 0.89, 0.94] | 72.79 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_Ins_r1 (c) |        0.14 | 0.03 | [ 0.08, 0.19] |  4.99 | < .001 |  1.00
## Approach =~ BWin_v_Neut_L_NAc_r1 (a) |        0.64 | 0.03 | [ 0.59, 0.70] | 24.37 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_NAc_r1     |        0.96 | 0.01 | [ 0.94, 0.98] | 92.73 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_Ins_r1 (c) |        0.11 | 0.02 | [ 0.07, 0.16] |  4.96 | < .001 |  1.00
## Approach =~ AWin_v_Neut_L_NAc_r2 (b) |        0.22 | 0.03 | [ 0.16, 0.28] |  7.47 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_NAc_r2 (e) |        0.13 | 0.03 | [ 0.07, 0.18] |  4.58 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_Ins_r2 (d) |        0.03 | 0.03 | [-0.02, 0.08] |  1.06 | 0.288  |  1.00
## Approach =~ BWin_v_Neut_L_NAc_r2 (b) |        0.19 | 0.03 | [ 0.14, 0.24] |  7.38 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_NAc_r2 (e) |        0.11 | 0.02 | [ 0.06, 0.16] |  4.56 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_Ins_r2 (d) |        0.02 | 0.02 | [-0.02, 0.07] |  1.06 | 0.288  |  1.00
## Approach =~ BWin_v_BLose_L_NAc_r2    |        0.01 | 0.06 | [-0.09, 0.12] |  0.26 | 0.793  |  1.00
## Approach =~ BWin_v_BLose_R_NAc_r2    |       -0.02 | 0.06 | [-0.13, 0.09] | -0.40 | 0.688  |  1.00
## Avoid =~ BLose_v_Neut_L_Ins_r1       |        0.96 | 0.01 | [ 0.94, 0.98] | 85.41 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_R_Ins_r1       |        0.67 | 0.03 | [ 0.61, 0.73] | 21.48 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_L_Ins_r1       |        0.38 | 0.05 | [ 0.29, 0.47] |  8.06 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_R_Ins_r1       |        0.20 | 0.05 | [ 0.10, 0.31] |  3.82 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_L_Ins_r2       |        0.15 | 0.05 | [ 0.04, 0.25] |  2.69 | 0.007  |  1.00
## Avoid =~ ALose_v_Neut_R_Ins_r2       |        0.13 | 0.05 | [ 0.02, 0.23] |  2.33 | 0.020  |  1.00
## Avoid =~ BLose_v_Neut_L_Ins_r2       |        0.10 | 0.05 | [-0.01, 0.21] |  1.80 | 0.072  |  1.00
## Avoid =~ BLose_v_Neut_R_Ins_r2       |        0.08 | 0.05 | [-0.03, 0.19] |  1.42 | 0.157  |  1.00
## Avoid =~ ALose_v_Neut_L_Ins_r1       |        0.92 | 0.01 | [ 0.89, 0.94] | 70.23 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_R_Ins_r1       |        0.64 | 0.03 | [ 0.57, 0.70] | 19.03 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_L_Ins_r2       |        0.01 | 0.06 | [-0.10, 0.12] |  0.21 | 0.833  |  1.00
## Avoid =~ BLose_v_BWin_R_Ins_r2       |        0.04 | 0.06 | [-0.07, 0.15] |  0.71 | 0.479  |  1.00
## Approach =~ BWin_v_BLose_L_NAc_r1    |        0.45 | 0.05 | [ 0.35, 0.55] |  8.75 | < .001 |  2.00
## Approach =~ BWin_v_BLose_R_NAc_r1    |        0.30 | 0.10 | [ 0.11, 0.49] |  3.10 | 0.002  |  2.00
## Approach =~ AWin_v_Neut_L_NAc_r1 (a) |        0.88 | 0.03 | [ 0.83, 0.94] | 32.41 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_NAc_r1     |        0.59 | 0.07 | [ 0.45, 0.73] |  8.15 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_Ins_r1 (c) |        0.22 | 0.05 | [ 0.13, 0.31] |  4.70 | < .001 |  2.00
## Approach =~ BWin_v_Neut_L_NAc_r1 (a) |        0.91 | 0.03 | [ 0.85, 0.96] | 34.74 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_NAc_r1     |        0.62 | 0.07 | [ 0.49, 0.75] |  9.10 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_Ins_r1 (c) |        0.18 | 0.04 | [ 0.10, 0.25] |  4.63 | < .001 |  2.00
## Approach =~ AWin_v_Neut_L_NAc_r2 (b) |        0.29 | 0.04 | [ 0.20, 0.38] |  6.52 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_NAc_r2 (e) |        0.19 | 0.04 | [ 0.11, 0.28] |  4.34 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_Ins_r2 (d) |        0.04 | 0.04 | [-0.04, 0.12] |  1.06 | 0.289  |  2.00
## Approach =~ BWin_v_Neut_L_NAc_r2 (b) |        0.23 | 0.04 | [ 0.16, 0.29] |  6.31 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_NAc_r2 (e) |        0.15 | 0.04 | [ 0.08, 0.22] |  4.28 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_Ins_r2 (d) |        0.03 | 0.03 | [-0.03, 0.10] |  1.06 | 0.290  |  2.00
## Approach =~ BWin_v_BLose_L_NAc_r2    |        0.10 | 0.11 | [-0.10, 0.31] |  0.99 | 0.320  |  2.00
## Approach =~ BWin_v_BLose_R_NAc_r2    |        0.02 | 0.11 | [-0.19, 0.23] |  0.20 | 0.840  |  2.00
## Avoid =~ BLose_v_Neut_L_Ins_r1       |        0.69 | 0.06 | [ 0.58, 0.80] | 12.38 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_R_Ins_r1       |        0.96 | 0.02 | [ 0.92, 0.99] | 52.84 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_L_Ins_r1       |        0.31 | 0.09 | [ 0.12, 0.49] |  3.25 | 0.001  |  2.00
## Avoid =~ BLose_v_BWin_R_Ins_r1       |        0.44 | 0.08 | [ 0.28, 0.61] |  5.22 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_L_Ins_r2       |        0.22 | 0.10 | [ 0.03, 0.42] |  2.27 | 0.023  |  2.00
## Avoid =~ ALose_v_Neut_R_Ins_r2       |        0.14 | 0.10 | [-0.06, 0.34] |  1.33 | 0.184  |  2.00
## Avoid =~ BLose_v_Neut_L_Ins_r2       |        0.13 | 0.10 | [-0.07, 0.33] |  1.32 | 0.188  |  2.00
## Avoid =~ BLose_v_Neut_R_Ins_r2       |        0.10 | 0.10 | [-0.10, 0.30] |  0.98 | 0.326  |  2.00
## Avoid =~ ALose_v_Neut_L_Ins_r1       |        0.69 | 0.06 | [ 0.58, 0.80] | 12.50 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_R_Ins_r1       |        0.94 | 0.02 | [ 0.90, 0.98] | 47.21 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_L_Ins_r2       |       -0.06 | 0.10 | [-0.26, 0.14] | -0.57 | 0.570  |  2.00
## Avoid =~ BLose_v_BWin_R_Ins_r2       |        0.03 | 0.10 | [-0.17, 0.23] |  0.30 | 0.764  |  2.00
## Approach =~ BWin_v_BLose_L_NAc_r1    |        0.53 | 0.05 | [ 0.43, 0.64] | 10.23 | < .001 |  3.00
## Approach =~ BWin_v_BLose_R_NAc_r1    |        0.48 | 0.08 | [ 0.33, 0.63] |  6.31 | < .001 |  3.00
## Approach =~ AWin_v_Neut_L_NAc_r1 (a) |        0.93 | 0.02 | [ 0.89, 0.97] | 51.75 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_NAc_r1     |        0.71 | 0.05 | [ 0.62, 0.81] | 14.29 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_Ins_r1 (c) |        0.21 | 0.04 | [ 0.12, 0.30] |  4.77 | < .001 |  3.00
## Approach =~ BWin_v_Neut_L_NAc_r1 (a) |        0.91 | 0.02 | [ 0.87, 0.95] | 46.28 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_NAc_r1     |        0.77 | 0.04 | [ 0.69, 0.85] | 18.28 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_Ins_r1 (c) |        0.18 | 0.04 | [ 0.10, 0.25] |  4.72 | < .001 |  3.00
## Approach =~ AWin_v_Neut_L_NAc_r2 (b) |        0.31 | 0.05 | [ 0.22, 0.40] |  6.86 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_NAc_r2 (e) |        0.19 | 0.04 | [ 0.10, 0.27] |  4.40 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_Ins_r2 (d) |        0.05 | 0.05 | [-0.04, 0.14] |  1.06 | 0.288  |  3.00
## Approach =~ BWin_v_Neut_L_NAc_r2 (b) |        0.28 | 0.04 | [ 0.20, 0.37] |  6.74 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_NAc_r2 (e) |        0.17 | 0.04 | [ 0.09, 0.24] |  4.37 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_Ins_r2 (d) |        0.04 | 0.04 | [-0.03, 0.11] |  1.06 | 0.289  |  3.00
## Approach =~ BWin_v_BLose_L_NAc_r2    |        0.16 | 0.10 | [-0.02, 0.35] |  1.70 | 0.089  |  3.00
## Approach =~ BWin_v_BLose_R_NAc_r2    |    6.14e-03 | 0.10 | [-0.19, 0.20] |  0.06 | 0.950  |  3.00
## Avoid =~ BLose_v_Neut_L_Ins_r1       |        0.99 | 0.01 | [ 0.97, 1.02] | 71.68 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_R_Ins_r1       |        0.65 | 0.06 | [ 0.54, 0.76] | 11.78 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_L_Ins_r1       |        0.63 | 0.06 | [ 0.51, 0.74] | 10.70 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_R_Ins_r1       |        0.36 | 0.08 | [ 0.20, 0.52] |  4.31 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_L_Ins_r2       |        0.03 | 0.09 | [-0.15, 0.22] |  0.34 | 0.733  |  3.00
## Avoid =~ ALose_v_Neut_R_Ins_r2       |        0.12 | 0.09 | [-0.07, 0.30] |  1.26 | 0.207  |  3.00
## Avoid =~ BLose_v_Neut_L_Ins_r2       |        0.06 | 0.09 | [-0.12, 0.25] |  0.66 | 0.510  |  3.00
## Avoid =~ BLose_v_Neut_R_Ins_r2       |        0.18 | 0.09 | [ 0.00, 0.36] |  1.92 | 0.055  |  3.00
## Avoid =~ ALose_v_Neut_L_Ins_r1       |        0.92 | 0.02 | [ 0.88, 0.95] | 46.05 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_R_Ins_r1       |        0.59 | 0.06 | [ 0.47, 0.71] |  9.40 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_L_Ins_r2       |   -7.92e-03 | 0.09 | [-0.19, 0.18] | -0.08 | 0.934  |  3.00
## Avoid =~ BLose_v_BWin_R_Ins_r2       |        0.06 | 0.09 | [-0.13, 0.25] |  0.63 | 0.529  |  3.00
## 
## # Correlation
## 
## Link              | Coefficient |   SE |        95% CI |    z |     p | Group
## -----------------------------------------------------------------------------
## Approach ~~ Avoid |        0.13 | 0.06 | [ 0.02, 0.24] | 2.39 | 0.017 |  1.00
## Approach ~~ Avoid |        0.19 | 0.11 | [-0.01, 0.40] | 1.83 | 0.068 |  2.00
## Approach ~~ Avoid |        0.15 | 0.10 | [-0.04, 0.34] | 1.59 | 0.112 |  3.00

config_params = data.frame(parameters(configural_cfa, standardize = T)) %>% 
  slice(1:29) %>% 
  select(-c("z","Component","Group","CI_low","CI_high")) %>% 
  rename("Fixed" = Label, "β" = Coefficient)

config_params$p <- if_else(config_params$p < .001, "< .001", 
                           if_else(config_params$p < .01, "< .01", 
                                   if_else(config_params$p < .05, "< .05", "> .05")))
config_params[,4:5] <- round(config_params[,c(4:5)],2)

# Report table
kable(config_params, booktabs = TRUE) %>%
  kable_styling(font_size = 12,position = 'center',html_font = "Times New Roman")

To	Operator	From	β	SE	p	Fixed
Approach	=~	BWin_v_BLose_L_NAc_r1	0.38	0.04	< .001
Approach	=~	BWin_v_BLose_R_NAc_r1	0.57	0.04	< .001
Approach	=~	AWin_v_Neut_L_NAc_r1	0.69	0.03	< .001	a
Approach	=~	AWin_v_Neut_R_NAc_r1	0.92	0.01	< .001
Approach	=~	AWin_v_Neut_R_Ins_r1	0.14	0.03	< .001	c
Approach	=~	BWin_v_Neut_L_NAc_r1	0.64	0.03	< .001	a
Approach	=~	BWin_v_Neut_R_NAc_r1	0.96	0.01	< .001
Approach	=~	BWin_v_Neut_R_Ins_r1	0.11	0.02	< .001	c
Approach	=~	AWin_v_Neut_L_NAc_r2	0.22	0.03	< .001	b
Approach	=~	AWin_v_Neut_R_NAc_r2	0.13	0.03	< .001	e
Approach	=~	AWin_v_Neut_R_Ins_r2	0.03	0.03	> .05	d
Approach	=~	BWin_v_Neut_L_NAc_r2	0.19	0.03	< .001	b
Approach	=~	BWin_v_Neut_R_NAc_r2	0.11	0.02	< .001	e
Approach	=~	BWin_v_Neut_R_Ins_r2	0.02	0.02	> .05	d
Approach	=~	BWin_v_BLose_L_NAc_r2	0.01	0.06	> .05
Approach	=~	BWin_v_BLose_R_NAc_r2	-0.02	0.06	> .05
Avoid	=~	BLose_v_Neut_L_Ins_r1	0.96	0.01	< .001
Avoid	=~	BLose_v_Neut_R_Ins_r1	0.67	0.03	< .001
Avoid	=~	BLose_v_BWin_L_Ins_r1	0.38	0.05	< .001
Avoid	=~	BLose_v_BWin_R_Ins_r1	0.20	0.05	< .001
Avoid	=~	ALose_v_Neut_L_Ins_r2	0.15	0.05	< .01
Avoid	=~	ALose_v_Neut_R_Ins_r2	0.13	0.05	< .05
Avoid	=~	BLose_v_Neut_L_Ins_r2	0.10	0.05	> .05
Avoid	=~	BLose_v_Neut_R_Ins_r2	0.08	0.05	> .05
Avoid	=~	ALose_v_Neut_L_Ins_r1	0.92	0.01	< .001
Avoid	=~	ALose_v_Neut_R_Ins_r1	0.64	0.03	< .001
Avoid	=~	BLose_v_BWin_L_Ins_r2	0.01	0.06	> .05
Avoid	=~	BLose_v_BWin_R_Ins_r2	0.04	0.06	> .05
Approach	~~	Avoid	0.13	0.06	< .05

4.5.1.3 Metric CFA model

##### Summarizing Metric Multi-group CFA model #####
parameters(metric_cfa, standardize = T)

## # Loading
## 
## Link                                      | Coefficient |   SE |        95% CI |     z |      p | Group
## -------------------------------------------------------------------------------------------------------
## Approach =~ BWin_v_BLose_L_NAc_r1         |        0.50 | 0.04 | [ 0.43, 0.57] | 13.73 | < .001 |  1.00
## Approach =~ BWin_v_BLose_R_NAc_r1 (.p2.)  |        0.44 | 0.04 | [ 0.37, 0.52] | 11.60 | < .001 |  1.00
## Approach =~ AWin_v_Neut_L_NAc_r1 (a)      |        0.90 | 0.01 | [ 0.88, 0.93] | 72.29 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_NAc_r1 (.p4.)   |        0.69 | 0.03 | [ 0.64, 0.74] | 25.12 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_Ins_r1 (c)      |        0.19 | 0.03 | [ 0.13, 0.26] |  5.91 | < .001 |  1.00
## Approach =~ BWin_v_Neut_L_NAc_r1 (a)      |        0.90 | 0.01 | [ 0.88, 0.93] | 71.51 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_NAc_r1 (.p7.)   |        0.72 | 0.03 | [ 0.67, 0.77] | 27.91 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_Ins_r1 (c)      |        0.16 | 0.03 | [ 0.10, 0.21] |  5.84 | < .001 |  1.00
## Approach =~ AWin_v_Neut_L_NAc_r2 (b)      |        0.29 | 0.03 | [ 0.23, 0.35] |  8.84 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_NAc_r2 (e)      |        0.19 | 0.03 | [ 0.12, 0.25] |  5.67 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_Ins_r2 (d)      |        0.05 | 0.03 | [-0.01, 0.11] |  1.66 | 0.097  |  1.00
## Approach =~ BWin_v_Neut_L_NAc_r2 (b)      |        0.25 | 0.03 | [ 0.20, 0.31] |  8.67 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_NAc_r2 (e)      |        0.16 | 0.03 | [ 0.10, 0.21] |  5.62 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_Ins_r2 (d)      |        0.04 | 0.03 | [-0.01, 0.10] |  1.66 | 0.097  |  1.00
## Approach =~ BWin_v_BLose_L_NAc_r2 (.p15.) |        0.10 | 0.04 | [ 0.02, 0.19] |  2.34 | 0.019  |  1.00
## Approach =~ BWin_v_BLose_R_NAc_r2 (.p16.) |        0.03 | 0.04 | [-0.05, 0.12] |  0.72 | 0.469  |  1.00
## Avoid =~ BLose_v_Neut_L_Ins_r1            |        0.96 | 0.01 | [ 0.94, 0.98] | 94.77 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_R_Ins_r1 (.p18.)    |        0.68 | 0.03 | [ 0.63, 0.73] | 25.01 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_L_Ins_r1 (.p19.)    |        0.43 | 0.04 | [ 0.36, 0.50] | 11.90 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_R_Ins_r1 (.p20.)    |        0.24 | 0.04 | [ 0.17, 0.31] |  6.31 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_L_Ins_r2 (.p21.)    |        0.12 | 0.04 | [ 0.05, 0.20] |  3.23 | 0.001  |  1.00
## Avoid =~ ALose_v_Neut_R_Ins_r2 (.p22.)    |        0.11 | 0.04 | [ 0.04, 0.18] |  2.88 | 0.004  |  1.00
## Avoid =~ BLose_v_Neut_L_Ins_r2 (.p23.)    |        0.08 | 0.04 | [ 0.01, 0.16] |  2.25 | 0.024  |  1.00
## Avoid =~ BLose_v_Neut_R_Ins_r2 (.p24.)    |        0.09 | 0.04 | [ 0.02, 0.16] |  2.40 | 0.016  |  1.00
## Avoid =~ ALose_v_Neut_L_Ins_r1 (.p25.)    |        0.91 | 0.01 | [ 0.89, 0.94] | 73.36 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_R_Ins_r1 (.p26.)    |        0.64 | 0.03 | [ 0.59, 0.70] | 22.01 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_L_Ins_r2 (.p27.)    |   -9.13e-03 | 0.04 | [-0.09, 0.07] | -0.23 | 0.818  |  1.00
## Avoid =~ BLose_v_BWin_R_Ins_r2 (.p28.)    |        0.03 | 0.04 | [-0.05, 0.10] |  0.68 | 0.498  |  1.00
## Approach =~ BWin_v_BLose_L_NAc_r1         |        0.44 | 0.05 | [ 0.35, 0.53] |  9.22 | < .001 |  2.00
## Approach =~ BWin_v_BLose_R_NAc_r1 (.p2.)  |        0.41 | 0.05 | [ 0.32, 0.51] |  8.51 | < .001 |  2.00
## Approach =~ AWin_v_Neut_L_NAc_r1 (a)      |        0.86 | 0.03 | [ 0.81, 0.92] | 28.76 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_NAc_r1 (.p4.)   |        0.60 | 0.05 | [ 0.51, 0.69] | 12.85 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_Ins_r1 (c)      |        0.22 | 0.04 | [ 0.14, 0.30] |  5.29 | < .001 |  2.00
## Approach =~ BWin_v_Neut_L_NAc_r1 (a)      |        0.88 | 0.03 | [ 0.83, 0.94] | 30.79 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_NAc_r1 (.p7.)   |        0.65 | 0.05 | [ 0.56, 0.74] | 14.39 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_Ins_r1 (c)      |        0.18 | 0.03 | [ 0.11, 0.24] |  5.22 | < .001 |  2.00
## Approach =~ AWin_v_Neut_L_NAc_r2 (b)      |        0.28 | 0.04 | [ 0.20, 0.36] |  7.04 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_NAc_r2 (e)      |        0.20 | 0.04 | [ 0.12, 0.28] |  5.09 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_Ins_r2 (d)      |        0.06 | 0.04 | [-0.01, 0.13] |  1.64 | 0.100  |  2.00
## Approach =~ BWin_v_Neut_L_NAc_r2 (b)      |        0.22 | 0.03 | [ 0.16, 0.28] |  6.82 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_NAc_r2 (e)      |        0.16 | 0.03 | [ 0.10, 0.22] |  5.02 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_Ins_r2 (d)      |        0.05 | 0.03 | [-0.01, 0.10] |  1.64 | 0.101  |  2.00
## Approach =~ BWin_v_BLose_L_NAc_r2 (.p15.) |        0.08 | 0.04 | [ 0.01, 0.16] |  2.28 | 0.023  |  2.00
## Approach =~ BWin_v_BLose_R_NAc_r2 (.p16.) |        0.03 | 0.04 | [-0.05, 0.11] |  0.72 | 0.471  |  2.00
## Avoid =~ BLose_v_Neut_L_Ins_r1            |        0.94 | 0.02 | [ 0.89, 0.98] | 41.58 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_R_Ins_r1 (.p18.)    |        0.62 | 0.05 | [ 0.53, 0.71] | 13.79 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_L_Ins_r1 (.p19.)    |        0.43 | 0.05 | [ 0.34, 0.53] |  8.94 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_R_Ins_r1 (.p20.)    |        0.28 | 0.05 | [ 0.18, 0.37] |  5.68 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_L_Ins_r2 (.p21.)    |        0.14 | 0.05 | [ 0.05, 0.23] |  3.12 | 0.002  |  2.00
## Avoid =~ ALose_v_Neut_R_Ins_r2 (.p22.)    |        0.11 | 0.04 | [ 0.03, 0.19] |  2.79 | 0.005  |  2.00
## Avoid =~ BLose_v_Neut_L_Ins_r2 (.p23.)    |        0.10 | 0.04 | [ 0.01, 0.18] |  2.21 | 0.027  |  2.00
## Avoid =~ BLose_v_Neut_R_Ins_r2 (.p24.)    |        0.09 | 0.04 | [ 0.02, 0.17] |  2.35 | 0.019  |  2.00
## Avoid =~ ALose_v_Neut_L_Ins_r1 (.p25.)    |        0.90 | 0.02 | [ 0.85, 0.95] | 36.65 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_R_Ins_r1 (.p26.)    |        0.59 | 0.05 | [ 0.50, 0.68] | 12.70 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_L_Ins_r2 (.p27.)    |       -0.01 | 0.04 | [-0.10, 0.08] | -0.23 | 0.818  |  2.00
## Avoid =~ BLose_v_BWin_R_Ins_r2 (.p28.)    |        0.03 | 0.04 | [-0.06, 0.12] |  0.68 | 0.499  |  2.00
## Approach =~ BWin_v_BLose_L_NAc_r1         |        0.52 | 0.05 | [ 0.43, 0.62] | 10.84 | < .001 |  3.00
## Approach =~ BWin_v_BLose_R_NAc_r1 (.p2.)  |        0.45 | 0.05 | [ 0.36, 0.55] |  9.36 | < .001 |  3.00
## Approach =~ AWin_v_Neut_L_NAc_r1 (a)      |        0.93 | 0.02 | [ 0.89, 0.96] | 50.61 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_NAc_r1 (.p4.)   |        0.74 | 0.04 | [ 0.66, 0.81] | 19.40 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_Ins_r1 (c)      |        0.21 | 0.04 | [ 0.14, 0.29] |  5.42 | < .001 |  3.00
## Approach =~ BWin_v_Neut_L_NAc_r1 (a)      |        0.90 | 0.02 | [ 0.86, 0.94] | 44.10 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_NAc_r1 (.p7.)   |        0.78 | 0.03 | [ 0.71, 0.85] | 22.57 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_Ins_r1 (c)      |        0.18 | 0.03 | [ 0.11, 0.25] |  5.35 | < .001 |  3.00
## Approach =~ AWin_v_Neut_L_NAc_r2 (b)      |        0.31 | 0.04 | [ 0.23, 0.39] |  7.48 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_NAc_r2 (e)      |        0.20 | 0.04 | [ 0.12, 0.27] |  5.22 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_Ins_r2 (d)      |        0.07 | 0.04 | [-0.01, 0.15] |  1.65 | 0.099  |  3.00
## Approach =~ BWin_v_Neut_L_NAc_r2 (b)      |        0.28 | 0.04 | [ 0.20, 0.35] |  7.36 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_NAc_r2 (e)      |        0.18 | 0.03 | [ 0.11, 0.24] |  5.17 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_Ins_r2 (d)      |        0.05 | 0.03 | [-0.01, 0.12] |  1.65 | 0.100  |  3.00
## Approach =~ BWin_v_BLose_L_NAc_r2 (.p15.) |        0.12 | 0.05 | [ 0.02, 0.22] |  2.31 | 0.021  |  3.00
## Approach =~ BWin_v_BLose_R_NAc_r2 (.p16.) |        0.03 | 0.05 | [-0.06, 0.13] |  0.72 | 0.470  |  3.00
## Avoid =~ BLose_v_Neut_L_Ins_r1            |        0.97 | 0.01 | [ 0.95, 1.00] | 74.52 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_R_Ins_r1 (.p18.)    |        0.70 | 0.04 | [ 0.62, 0.78] | 17.95 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_L_Ins_r1 (.p19.)    |        0.51 | 0.05 | [ 0.42, 0.61] | 10.41 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_R_Ins_r1 (.p20.)    |        0.32 | 0.05 | [ 0.22, 0.43] |  6.00 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_L_Ins_r2 (.p21.)    |        0.18 | 0.06 | [ 0.07, 0.29] |  3.19 | 0.001  |  3.00
## Avoid =~ ALose_v_Neut_R_Ins_r2 (.p22.)    |        0.17 | 0.06 | [ 0.05, 0.29] |  2.86 | 0.004  |  3.00
## Avoid =~ BLose_v_Neut_L_Ins_r2 (.p23.)    |        0.13 | 0.06 | [ 0.02, 0.25] |  2.24 | 0.025  |  3.00
## Avoid =~ BLose_v_Neut_R_Ins_r2 (.p24.)    |        0.15 | 0.06 | [ 0.03, 0.27] |  2.40 | 0.017  |  3.00
## Avoid =~ ALose_v_Neut_L_Ins_r1 (.p25.)    |        0.93 | 0.02 | [ 0.90, 0.96] | 56.84 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_R_Ins_r1 (.p26.)    |        0.68 | 0.04 | [ 0.60, 0.76] | 16.52 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_L_Ins_r2 (.p27.)    |       -0.01 | 0.05 | [-0.12, 0.09] | -0.23 | 0.818  |  3.00
## Avoid =~ BLose_v_BWin_R_Ins_r2 (.p28.)    |        0.04 | 0.06 | [-0.07, 0.15] |  0.68 | 0.498  |  3.00
## 
## # Correlation
## 
## Link              | Coefficient |   SE |        95% CI |    z |     p | Group
## -----------------------------------------------------------------------------
## Approach ~~ Avoid |        0.17 | 0.06 | [ 0.06, 0.28] | 2.98 | 0.003 |  1.00
## Approach ~~ Avoid |        0.11 | 0.11 | [-0.11, 0.33] | 1.00 | 0.315 |  2.00
## Approach ~~ Avoid |        0.17 | 0.10 | [-0.02, 0.36] | 1.73 | 0.083 |  3.00

metric_params = data.frame(parameters(metric_cfa, standardize = T)) %>% 
  slice(1:29) %>% 
  select(-c("z","Component","Group","CI_low","CI_high")) %>% 
  rename("Fixed" = Label, "β" = Coefficient)

metric_params$p <- if_else(metric_params$p < .001, "< .001", 
                           if_else(metric_params$p < .01, "< .01", 
                                   if_else(metric_params$p < .05, "< .05", "> .05")))
metric_params[,4:5] <- round(metric_params[,c(4:5)],2)

# Report table
kable(metric_params, booktabs = TRUE) %>%
  kable_styling(font_size = 12,position = 'center',html_font = "Times New Roman")

To	Operator	From	β	SE	p	Fixed
Approach	=~	BWin_v_BLose_L_NAc_r1	0.50	0.04	< .001
Approach	=~	BWin_v_BLose_R_NAc_r1	0.44	0.04	< .001	.p2.
Approach	=~	AWin_v_Neut_L_NAc_r1	0.90	0.01	< .001	a
Approach	=~	AWin_v_Neut_R_NAc_r1	0.69	0.03	< .001	.p4.
Approach	=~	AWin_v_Neut_R_Ins_r1	0.19	0.03	< .001	c
Approach	=~	BWin_v_Neut_L_NAc_r1	0.90	0.01	< .001	a
Approach	=~	BWin_v_Neut_R_NAc_r1	0.72	0.03	< .001	.p7.
Approach	=~	BWin_v_Neut_R_Ins_r1	0.16	0.03	< .001	c
Approach	=~	AWin_v_Neut_L_NAc_r2	0.29	0.03	< .001	b
Approach	=~	AWin_v_Neut_R_NAc_r2	0.19	0.03	< .001	e
Approach	=~	AWin_v_Neut_R_Ins_r2	0.05	0.03	> .05	d
Approach	=~	BWin_v_Neut_L_NAc_r2	0.25	0.03	< .001	b
Approach	=~	BWin_v_Neut_R_NAc_r2	0.16	0.03	< .001	e
Approach	=~	BWin_v_Neut_R_Ins_r2	0.04	0.03	> .05	d
Approach	=~	BWin_v_BLose_L_NAc_r2	0.10	0.04	< .05	.p15.
Approach	=~	BWin_v_BLose_R_NAc_r2	0.03	0.04	> .05	.p16.
Avoid	=~	BLose_v_Neut_L_Ins_r1	0.96	0.01	< .001
Avoid	=~	BLose_v_Neut_R_Ins_r1	0.68	0.03	< .001	.p18.
Avoid	=~	BLose_v_BWin_L_Ins_r1	0.43	0.04	< .001	.p19.
Avoid	=~	BLose_v_BWin_R_Ins_r1	0.24	0.04	< .001	.p20.
Avoid	=~	ALose_v_Neut_L_Ins_r2	0.12	0.04	< .01	.p21.
Avoid	=~	ALose_v_Neut_R_Ins_r2	0.11	0.04	< .01	.p22.
Avoid	=~	BLose_v_Neut_L_Ins_r2	0.08	0.04	< .05	.p23.
Avoid	=~	BLose_v_Neut_R_Ins_r2	0.09	0.04	< .05	.p24.
Avoid	=~	ALose_v_Neut_L_Ins_r1	0.91	0.01	< .001	.p25.
Avoid	=~	ALose_v_Neut_R_Ins_r1	0.64	0.03	< .001	.p26.
Avoid	=~	BLose_v_BWin_L_Ins_r2	-0.01	0.04	> .05	.p27.
Avoid	=~	BLose_v_BWin_R_Ins_r2	0.03	0.04	> .05	.p28.
Approach	~~	Avoid	0.17	0.06	< .01

4.6 ANOVA: Comparing models

4.6.1 Strict v Configural

The below compares whether the combined data (across all three samples) in the all_cfa (strict, comined data) model is significantly improved by the configural invariance model (relaxing all constraints, item loadings, intercepts and residual variances, except factor structure). A significant value indicates that the reduction in the chi-square statistic is meaningfully different between the two models the model with lower BIC is a better fit.

anova(all_sample, configural_cfa)

## Chi-Squared Difference Test
## 
##                  Df     AIC     BIC Chisq Chisq diff Df diff Pr(>Chisq)
## all_sample      354 -7940.1 -7594.5 23971                              
## configural_cfa 1072 -8125.1 -7131.7 24734     762.76     718       0.12

4.7 Plot Configural MG-CFA

Use semPaths to plot the configural invariance CFA multigroup model

# this plottinig is not function with runs loading onto ROIs

layout(t(1:3))
semPaths(configural_cfa,
         color = "lightyellow",
         theme="colorblind",
         whatLabels = "std",
         style = "lisrel",
         sizeLat = 10,
         sizeLat2 = 10,
         sizeMan = 6,
         edge.color = "steelblue",
         edge.label.cex = 2,
         label.cex = 2,
         rotation = 2,
         layout = "tree2",
         intercepts = TRUE,
         residuals = FALSE,
         #residScale = 10,
         curve = 2,
         title = T,
         title.color = "black",
         cardinal = "lat cov",
         curvePivot = T,
         nCharNodes = 6,
         #nodeLabels = label,
         mar = c(1,3,1,3))

5 Exploratory SEM

Exploratory Structural Equation Modeling (ESEM): As described in March et al. (2014), create a target rotation for items onto factors. First, to keep consistent with the Stage 1 Registered report extract the variable names:

esem_data = brain_set[,c("AWin_v_Neut_L_NAc_r1"  ,"AWin_v_Neut_L_NAc_r2" ,
                         "BWin_v_Neut_L_NAc_r1"  ,"BWin_v_Neut_L_NAc_r2" ,
                         "BWin_v_BLose_L_NAc_r1" ,"BWin_v_BLose_L_NAc_r2",
                          "AWin_v_Neut_R_NAc_r1" , "AWin_v_Neut_R_NAc_r2",
                          "BWin_v_Neut_R_NAc_r1" , "BWin_v_Neut_R_NAc_r2",
                          "BWin_v_BLose_R_NAc_r1", "BWin_v_BLose_R_NAc_r2",
                         # Ins values apprach 
                         "AWin_v_Neut_R_Ins_r1","AWin_v_Neut_R_Ins_r2", 
                         "BWin_v_Neut_R_Ins_r1","BWin_v_Neut_R_Ins_r2", 
                         # avoidance
                         "ALose_v_Neut_L_Ins_r1","ALose_v_Neut_L_Ins_r2",
                         "BLose_v_Neut_L_Ins_r1","BLose_v_Neut_L_Ins_r2",
                         "BLose_v_BWin_L_Ins_r1","BLose_v_BWin_L_Ins_r2",
                         "ALose_v_Neut_R_Ins_r1","ALose_v_Neut_R_Ins_r2",
                         "BLose_v_Neut_R_Ins_r1","BLose_v_Neut_R_Ins_r2",
                         "BLose_v_BWin_R_Ins_r1","BLose_v_BWin_R_Ins_r2",
                         "set")]

5.1 Targets/Anchor/Model

In this case two factors are specified by the CFA model, so factor 1 and factor 2 are specified in make_target.

target_rot <- make_target(28,mainloadings = list(f1 = 1:16, f2 = 17:28))
esem.efa <- esem_efa(data = esem_data[,1:28], nfactors = 2,
                     target = target_rot, fm = "ml")

## Loading required namespace: GPArotation

esem.efa$loadings

## 
## Loadings:
##                       ML2    ML1   
## AWin_v_Neut_L_NAc_r1   0.147  0.241
## AWin_v_Neut_L_NAc_r2          0.917
## BWin_v_Neut_L_NAc_r1   0.139  0.302
## BWin_v_Neut_L_NAc_r2          0.943
## BWin_v_BLose_L_NAc_r1         0.180
## BWin_v_BLose_L_NAc_r2 -0.127  0.441
## AWin_v_Neut_R_NAc_r1   0.135  0.237
## AWin_v_Neut_R_NAc_r2          0.672
## BWin_v_Neut_R_NAc_r1   0.123  0.283
## BWin_v_Neut_R_NAc_r2          0.695
## BWin_v_BLose_R_NAc_r1         0.173
## BWin_v_BLose_R_NAc_r2 -0.125  0.321
## AWin_v_Neut_R_Ins_r1   0.677       
## AWin_v_Neut_R_Ins_r2   0.137  0.242
## BWin_v_Neut_R_Ins_r1   0.627       
## BWin_v_Neut_R_Ins_r2          0.255
## ALose_v_Neut_L_Ins_r1  0.693       
## ALose_v_Neut_L_Ins_r2  0.205  0.128
## BLose_v_Neut_L_Ins_r1  0.695       
## BLose_v_Neut_L_Ins_r2  0.186  0.107
## BLose_v_BWin_L_Ins_r1  0.262       
## BLose_v_BWin_L_Ins_r2        -0.209
## ALose_v_Neut_R_Ins_r1  0.923       
## ALose_v_Neut_R_Ins_r2  0.193  0.158
## BLose_v_Neut_R_Ins_r1  0.896       
## BLose_v_Neut_R_Ins_r2  0.181  0.118
## BLose_v_BWin_R_Ins_r1  0.222       
## BLose_v_BWin_R_Ins_r2  0.104 -0.134
## 
##                  ML2   ML1
## SS loadings    3.888 3.567
## Proportion Var 0.139 0.127
## Cumulative Var 0.139 0.266

Using item that loads highest on factor 1 and lowest on factor 2 and vice versa, and define as anchor using find_referents

# per the example from Mateus Silverstrin, need to define anchor for each factor (value to loads highers on 1 factor and lowest on other)
anchor <- find_referents(efa_object = esem.efa,
                         factor_names = c("f1","f2"))

Once the esem efa and anchors are defined, use syntax_composer to specify the esem model. This will produce a lavaan specified model that references starting values that will be used in the cfa model

# Pull starting parameters
esem_mid_model <- syntax_composer(efa_object = esem.efa, referents = anchor)

5.2 Run ESEM

5.2.1 Print model

The starting values are printed below to provide reference for how starting values differ from a strict CFA model. Notice, how some values that were originally not fit onto the Approach factor (f1), such as big lose contrasts, they are now specified with loading values that are between .05 to -.05.

cat(esem_mid_model)

## f1 =~ start(0.147)*AWin_v_Neut_L_NAc_r1+
## start(-0.043)*AWin_v_Neut_L_NAc_r2+
## start(0.139)*BWin_v_Neut_L_NAc_r1+
## -0.04*BWin_v_Neut_L_NAc_r2+
## start(-0.031)*BWin_v_BLose_L_NAc_r1+
## start(-0.127)*BWin_v_BLose_L_NAc_r2+
## start(0.135)*AWin_v_Neut_R_NAc_r1+
## start(-0.026)*AWin_v_Neut_R_NAc_r2+
## start(0.123)*BWin_v_Neut_R_NAc_r1+
## start(-0.047)*BWin_v_Neut_R_NAc_r2+
## start(0.016)*BWin_v_BLose_R_NAc_r1+
## start(-0.125)*BWin_v_BLose_R_NAc_r2+
## start(0.677)*AWin_v_Neut_R_Ins_r1+
## start(0.137)*AWin_v_Neut_R_Ins_r2+
## start(0.627)*BWin_v_Neut_R_Ins_r1+
## start(0.089)*BWin_v_Neut_R_Ins_r2+
## start(0.693)*ALose_v_Neut_L_Ins_r1+
## start(0.205)*ALose_v_Neut_L_Ins_r2+
## start(0.695)*BLose_v_Neut_L_Ins_r1+
## start(0.186)*BLose_v_Neut_L_Ins_r2+
## start(0.262)*BLose_v_BWin_L_Ins_r1+
## start(0.061)*BLose_v_BWin_L_Ins_r2+
## start(0.923)*ALose_v_Neut_R_Ins_r1+
## start(0.193)*ALose_v_Neut_R_Ins_r2+
## start(0.896)*BLose_v_Neut_R_Ins_r1+
## start(0.181)*BLose_v_Neut_R_Ins_r2+
## start(0.222)*BLose_v_BWin_R_Ins_r1+
## start(0.104)*BLose_v_BWin_R_Ins_r2 
## 
## f2 =~ start(0.241)*AWin_v_Neut_L_NAc_r1+
## start(0.917)*AWin_v_Neut_L_NAc_r2+
## start(0.302)*BWin_v_Neut_L_NAc_r1+
## start(0.943)*BWin_v_Neut_L_NAc_r2+
## start(0.18)*BWin_v_BLose_L_NAc_r1+
## start(0.441)*BWin_v_BLose_L_NAc_r2+
## start(0.237)*AWin_v_Neut_R_NAc_r1+
## start(0.672)*AWin_v_Neut_R_NAc_r2+
## start(0.283)*BWin_v_Neut_R_NAc_r1+
## start(0.695)*BWin_v_Neut_R_NAc_r2+
## start(0.173)*BWin_v_BLose_R_NAc_r1+
## start(0.321)*BWin_v_BLose_R_NAc_r2+
## start(0.003)*AWin_v_Neut_R_Ins_r1+
## start(0.242)*AWin_v_Neut_R_Ins_r2+
## start(0.043)*BWin_v_Neut_R_Ins_r1+
## start(0.255)*BWin_v_Neut_R_Ins_r2+
## start(0.004)*ALose_v_Neut_L_Ins_r1+
## start(0.128)*ALose_v_Neut_L_Ins_r2+
## start(0.002)*BLose_v_Neut_L_Ins_r1+
## start(0.107)*BLose_v_Neut_L_Ins_r2+
## start(-0.037)*BLose_v_BWin_L_Ins_r1+
## start(-0.209)*BLose_v_BWin_L_Ins_r2+
## -0.022*ALose_v_Neut_R_Ins_r1+
## start(0.158)*ALose_v_Neut_R_Ins_r2+
## start(-0.011)*BLose_v_Neut_R_Ins_r1+
## start(0.118)*BLose_v_Neut_R_Ins_r2+
## start(-0.054)*BLose_v_BWin_R_Ins_r1+
## start(-0.134)*BLose_v_BWin_R_Ins_r2

5.2.2 Run full ESEM

After the EFA loadings are extracted using a target rotation, starting values are now available. These are now used to specify a less restrictive CFA model

esem_mid_fit<- cfa(esem_mid_model, esem_data[,1:28], 
                  estimator = "ML", std.lv = FALSE, 
                  meanstructure = TRUE, check.gradient = FALSE)

5.3 Extract Fit ESEM

Pull and add fit statistics to the out dataframe and print results to see decreases in AIC/BIC

# adding values to the CFA model fit indices
out[4,2:8] <- round(data.matrix(
  fitmeasures(esem_mid_fit, fit.measures = c("chisq","df","pvalue","rmsea", "srmr", "tli", "cfi"))), digits=2)
out[4,9] <- round(AIC(esem_mid_fit),0)
out[4,10] <- round(BIC(esem_mid_fit),0)
out[4,1] <-  c("Overall ESEM")

5.4 ANOVA: Strct v Strict ESEM

compared strict esem model versus strict model. The model fit suggests that the combined sample CFA model (-7594) is a better fit of the data than the over-parametized ESEM model (BIC -8011).

anova(all_sample, esem_mid_fit)

## Chi-Squared Difference Test
## 
##               Df     AIC     BIC Chisq Chisq diff Df diff Pr(>Chisq)    
## esem_mid_fit 323 -8490.9 -8011.5 23358                                  
## all_sample   354 -7940.1 -7594.5 23971     612.82      31  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

6 Table: CFA + ESEM Fit Stats

Reporting the complete set of fit statistics from to the overall CFA (combined data, strict model), the Configural CFA model, the Metric CFA model and the overall ESEM model (combined data).

kable(as.data.frame(out), booktabs = TRUE) %>%
  kable_styling(font_size = 12,position = 'center',html_font = "Times New Roman")

	χ2	DF	p-value	RMSEA	SRMR	TLI	CFI	AIC	BIC
Overall CFA	23971.19	354	0	0.35	0.2	0.06	0.12	-7940	-7595
Configg MG-CFA	24733.94	1072	0	0.35	0.21	0.07	0.12	-8125	-7132
Metric MG-CFA	24856.66	1104	0	0.34	0.21	0.1	0.12	-8066	-7211
Overall ESEM	23358.37	323	0	0.36	0.18	0	0.14	-8491	-8011

7 EFA Model

7.1 Identify # Factors

Using fa.parallel package to perform a parallel analysis to derive the recommended factors for the EFA model for each sample. To avoid biasing due different calculations across packages RE: recommendation factors, also using nFactors and the paran package. BIC estimates are also extracted to evaluate when they plateau. The statistics are used in aggregate to inform the final factor # for each sample.

7.1.1 ABCD factors

set.seed(111)
# fa parallel
fa.parallel(abcd_df[,mod_vars], fm = 'ml') # https://cran.r-project.org/web/packages/nFactors/nFactors.pdf

## Parallel analysis suggests that the number of factors =  8  and the number of components =  6

# nFactors
plot(nScree(x=abcd_df[,mod_vars], 
            cor = TRUE, model="factors"))

# paran(
paran(abcd_df[,mod_vars],
      iterations = 1000, quietly = FALSE, centile = 95, 
      status = FALSE, all = TRUE, cfa = TRUE, graph = TRUE, color = TRUE, 
      col = c("black", "red", "blue"), lty = c(1, 2, 3), lwd = 1, legend = TRUE, 
      seed = 100)

## 
## Using eigendecomposition of correlation matrix.
## 
## Results of Horn's Parallel Analysis for factor retention
## 1000 iterations, using the 95 centile estimate
## 
## -------------------------------------------------- 
## Factor      Adjusted    Unadjusted    Estimated 
##             Eigenvalue  Eigenvalue    Bias 
## -------------------------------------------------- 
## No components passed. 
## -------------------------------------------------- 
## 1           4.452297    5.193091      0.740794
## 2           3.829733    4.460029      0.630296
## 3           3.118505    3.677671      0.559166
## 4           2.551528    3.053299      0.501770
## 5           1.481765    1.930442      0.448676
## 6           1.337449    1.735678      0.398229
## 7           0.464809    0.816054      0.351244
## 8           0.408794    0.718397      0.309603
## 9           0.362692    0.635651      0.272958
## 10          0.399905    0.634724      0.234819
## 11          0.354860    0.553250      0.198390
## 12          0.323936    0.486268      0.162332
## 13          0.016893    0.144152      0.127258
## 14          0.041660    0.134358      0.092697
## 15          0.033370    0.095093      0.061723
## 16          0.037771    0.069294      0.031523
## 17          0.040902    0.038137     -0.00276
## 18          0.047132    0.017191     -0.02994
## 19          0.059039   -3.06010     -0.05904
## 20          0.088434   -3.43198     -0.08843
## 21          0.110808   -0.00787     -0.11868
## 22          0.131819   -0.01443     -0.14625
## 23          0.145728   -0.02892     -0.17465
## 24          0.159789   -0.04335     -0.20314
## 25          0.169442   -0.06417     -0.23362
## 26          0.189326   -0.07205     -0.26138
## 27          0.180793   -0.11371     -0.29450
## 28          0.205564   -0.12454     -0.33010
## -------------------------------------------------- 
## 
## Adjusted eigenvalues > 0 indicate dimensions to retain.
## (28 factors    retained)

# BIC
rec_factors <- matrix(NA, ncol = 2, nrow = 14)
colnames(rec_factors) <- c("Nfactors","BIC")

for (f in 1:14) {
  test_fac <- fa(abcd_df[,mod_vars],
                 nfactors = f, 
                 rotate = "promax", fm = "ml")
  rec_factors[f,1] <- f
  rec_factors[f,2] <-test_fac$BIC
}

bic_fact = as.data.frame(rec_factors)

lowest_bic <- which.min(bic_fact$BIC)

bic_fact %>% 
  ggplot(aes(x = Nfactors, y = BIC)) +
  geom_line(colour = 'black', linetype = 'dashed') +
  geom_vline(xintercept = bic_fact$Nfactors[lowest_bic], colour = 'red')+
  theme_minimal()

7.1.2 AHRB factors

set.seed(111)
# fa parallel
fa.parallel(ahrb_df[,mod_vars], fm = 'ml') # https://cran.r-project.org/web/packages/nFactors/nFactors.pdf

## Parallel analysis suggests that the number of factors =  6  and the number of components =  6

# nFactors
plot(nScree(x=ahrb_df[,mod_vars], model="factors"))

# paran(
paran(ahrb_df[,mod_vars],
      iterations = 1000, quietly = FALSE, centile = 95, 
      status = FALSE, all = TRUE, cfa = TRUE, graph = TRUE, color = TRUE, 
      col = c("black", "red", "blue"), lty = c(1, 2, 3), lwd = 1, legend = TRUE, 
      seed = 100)

## 
## Using eigendecomposition of correlation matrix.
## 
## Results of Horn's Parallel Analysis for factor retention
## 1000 iterations, using the 95 centile estimate
## 
## -------------------------------------------------- 
## Factor      Adjusted    Unadjusted    Estimated 
##             Eigenvalue  Eigenvalue    Bias 
## -------------------------------------------------- 
## 1           3.938196    5.620042      1.681845
## 2           2.751380    4.181203      1.429823
## 3           2.203102    3.459244      1.256142
## 4           1.594986    2.706708      1.111721
## 5           0.855493    1.845586      0.990092
## 6           0.743489    1.636668      0.893179
## 7           0.308646    1.103820      0.795173
## 8           0.330413    1.041210      0.710797
## 9           0.204873    0.832030      0.627157
## 10          0.026178    0.577381      0.551202
## 11          0.046761    0.523594      0.476832
## 12          0.051445    0.455954      0.404508
## 13         -0.152625    0.180371      0.332996
## 14         -0.094046    0.173871      0.267917
## 15         -0.063549    0.143658      0.207207
## 16         -0.042444    0.107588      0.150032
## 17         -0.034834    0.059581      0.094415
## 18         -0.016367    0.024053      0.040421
## 19          0.031155    0.014737     -0.01641
## 20          0.064656   -3.72445     -0.06466
## 21          0.114151   -5.38750     -0.11415
## 22          0.141438   -0.01974     -0.16118
## 23          0.179337   -0.02250     -0.20183
## 24          0.197675   -0.04749     -0.24516
## 25          0.231218   -0.05723     -0.28845
## 26          0.255588   -0.07189     -0.32748
## 27          0.266581   -0.10102     -0.36760
## 28          0.298788   -0.10909     -0.40788
## -------------------------------------------------- 
## 
## Adjusted eigenvalues > 0 indicate dimensions to retain.
## (12 factors    retained)

# BIC
rec_factors <- matrix(NA, ncol = 2, nrow = 14)
colnames(rec_factors) <- c("Nfactors","BIC")

for (f in 1:14) {
  test_fac <- fa(ahrb_df[,mod_vars],
                 nfactors = f, 
                 rotate = "promax", fm = "ml")
  rec_factors[f,1] <- f
  rec_factors[f,2] <-test_fac$BIC
}

bic_fact = as.data.frame(rec_factors)

lowest_bic <- which.min(bic_fact$BIC)

bic_fact %>% 
  ggplot(aes(x = Nfactors, y = BIC)) +
  geom_line(colour = 'black', linetype = 'dashed') +
  geom_vline(xintercept = bic_fact$Nfactors[lowest_bic], colour = 'red')+
  theme_minimal()

7.1.3 MLS factors

set.seed(111)
# fa parallel
fa.parallel(mls_df[,mod_vars], fm = 'ml') 

## Parallel analysis suggests that the number of factors =  7  and the number of components =  7

# nFactors
plot(nScree(mls_df[,mod_vars], model="factors"))

# paran(
paran(mls_df[,mod_vars],
      iterations = 1000, quietly = FALSE, centile = 95, 
      status = FALSE, all = TRUE, cfa = TRUE, graph = TRUE, color = TRUE, 
      col = c("black", "red", "blue"), lty = c(1, 2, 3), lwd = 1, legend = TRUE, 
      seed = 100)

## 
## Using eigendecomposition of correlation matrix.
## 
## Results of Horn's Parallel Analysis for factor retention
## 1000 iterations, using the 95 centile estimate
## 
## -------------------------------------------------- 
## Factor      Adjusted    Unadjusted    Estimated 
##             Eigenvalue  Eigenvalue    Bias 
## -------------------------------------------------- 
## 1           3.985681    5.500602      1.514920
## 2           2.436340    3.722389      1.286049
## 3           2.303270    3.439470      1.136199
## 4           1.814613    2.824675      1.010061
## 5           1.123006    2.031780      0.908774
## 6           0.890783    1.710398      0.819615
## 7           0.584453    1.308362      0.723908
## 8           0.262536    0.906576      0.644039
## 9           0.279573    0.846323      0.566749
## 10          0.249759    0.744132      0.494373
## 11          0.147317    0.569303      0.421985
## 12          0.048103    0.407903      0.359800
## 13         -0.000692    0.294085      0.294778
## 14         -0.090416    0.148116      0.238532
## 15         -0.050547    0.129233      0.179780
## 16         -0.045425    0.077642      0.123067
## 17         -0.004361    0.067979      0.072340
## 18         -0.001497    0.021483      0.022980
## 19          0.044565    0.016646     -0.02791
## 20          0.076680   -2.65471     -0.07668
## 21          0.121471   -3.12581     -0.12147
## 22          0.149710   -0.01751     -0.16722
## 23          0.186381   -0.02155     -0.20793
## 24          0.204028   -0.04571     -0.24974
## 25          0.231702   -0.05907     -0.29077
## 26          0.259872   -0.06961     -0.32948
## 27          0.267178   -0.10160     -0.36878
## 28          0.297083   -0.11196     -0.40904
## -------------------------------------------------- 
## 
## Adjusted eigenvalues > 0 indicate dimensions to retain.
## (12 factors    retained)

# BIC
rec_factors <- matrix(NA, ncol = 2, nrow = 14)
colnames(rec_factors) <- c("Nfactors","BIC")

for (f in 1:14) {
  test_fac <- fa(mls_df[,mod_vars],
                 nfactors = f, 
                 rotate = "promax", fm = "ml")
  rec_factors[f,1] <- f
  rec_factors[f,2] <-test_fac$BIC
}

bic_fact = as.data.frame(rec_factors)

lowest_bic <- which.min(bic_fact$BIC)

bic_fact %>% 
  ggplot(aes(x = Nfactors, y = BIC)) +
  geom_line(colour = 'black', linetype = 'dashed') +
  geom_vline(xintercept = bic_fact$Nfactors[lowest_bic], colour = 'red')+
  theme_minimal()

7.2 Run EFA

Used the (factanal)[https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/factanal] to run EFA model. Specifying the number of factors and using the promax (non-orthogonal) rotation w/ Maximum Likelihood Estimator.

efa_rownames = c(
  #Nacc
  "1. R1: All Win > $0 L-NAc", "2. R1: All Win > $0 R-NAc",
  "3. R2: All Win > $0 L-NAc", "4. R2: All Win > $0 R-NAc",
  "5. R1: Big Win > $0 L-NAc", "6. R1: Big Win > $0 R-NAc",
  "7. R2: Big Win > $0 L-NAc", "8. R2: Big Win > $0 R-NAc",
  "9. R1: Big Win > Big Lose L-NAc", "10. R1: Big Win > Big Lose R-NAc",
  "11. R2: Big Win > Big Lose L-NAc","12. R2: Big Win > Big Lose R-NAc",
  # Ins
  "13. R1: All Win > $0 R-Ins", "14. R2: All Win > $0 R-Ins",
  "15. R1: Big Win > $0 R-Ins", "16. R2: Big Win > $0 R-Ins",
  "17. R1: All Lose > $0 L-Ins", "18. R1: All Lose > $0 R-Ins",
  "19. R2: All Lose > $0 L-Ins", "20. R2: All Lose > $0 R-Ins",
  "21. R1: Big Lose > $0 L-Ins", "22. R1: Big Lose > $0 R-Ins",
  "23. R2: Big Lose > $0 L-Ins", "24. R2: Big Lose > $0 R-Ins",
  "25. R1: Big Lose > Big Win L-Ins", "26. R1: Big Lose > Big Win R-Ins",
  "27. R2: Big Lose > Big Win L-Ins", "28. R2: Big Lose > Big Win R-Ins"
)

7.2.1 ABCD EFA

abcd_factors = 6

abcd_efa = fa(abcd_df[,mod_vars], nfactors = abcd_factors,
              rotate = 'Promax', fm = 'ml')

abcd_colnames = paste("AD",1:abcd_efa$factors)

colnames(abcd_efa$loadings) <- abcd_colnames
model_parameters(abcd_efa)

## # Rotated loadings from Factor Analysis (Promax-rotation)
## 
## Variable              |   AD 1    |   AD 2   |   AD 3    |   AD 4    |   AD 5    |   AD 6    | Complexity | Uniqueness
## ----------------------------------------------------------------------------------------------------------------------
## AWin_v_Neut_L_NAc_r1  | -3.37e-03 |   0.09   |   0.06    |   0.60    |   0.06    |   -0.04   |    1.10    |    0.61   
## AWin_v_Neut_R_NAc_r1  |   -0.05   |  -0.01   |   -0.06   |   0.97    |   0.12    |   -0.02   |    1.04    |    0.15   
## AWin_v_Neut_L_NAc_r2  | -3.42e-04 |   0.03   |   0.94    |   0.01    |   0.02    |   0.07    |    1.02    |    0.15   
## AWin_v_Neut_R_NAc_r2  |   0.13    |  -0.04   |   0.66    |   0.01    | 1.29e-03  |   0.03    |    1.09    |    0.52   
## BWin_v_Neut_L_NAc_r1  | -4.58e-03 |   0.06   |   0.11    |   0.63    |   -0.02   |   -0.02   |    1.09    |    0.54   
## BWin_v_Neut_R_NAc_r1  |   -0.02   |  -0.03   |   -0.02   |   0.99    |   0.05    |   -0.03   |    1.01    |    0.07   
## BWin_v_Neut_L_NAc_r2  | 8.93e-04  |   0.04   |   0.99    |   -0.03   |   -0.01   |   0.05    |    1.01    |    0.07   
## BWin_v_Neut_R_NAc_r2  |   0.09    |  -0.05   |   0.67    | 7.03e-03  | 3.29e-04  | 5.24e-03  |    1.05    |    0.52   
## BWin_v_BLose_L_NAc_r1 | 8.48e-03  |  -0.13   |   0.09    |   0.29    |   -0.27   | 6.88e-03  |    2.57    |    0.76   
## BWin_v_BLose_R_NAc_r1 |   -0.02   |  -0.10   |   0.04    |   0.52    |   -0.16   |   0.02    |    1.28    |    0.64   
## BWin_v_BLose_L_NAc_r2 |   -0.18   |   0.01   |   0.50    |   -0.12   |   0.03    |   -0.08   |    1.47    |    0.71   
## BWin_v_BLose_R_NAc_r2 |   -0.19   |  -0.06   |   0.38    |   -0.12   |   0.02    |   -0.12   |    1.95    |    0.78   
## AWin_v_Neut_R_Ins_r1  |   -0.03   |   0.64   | -4.56e-03 |   -0.07   |   -0.57   | 1.89e-03  |    2.00    |    0.21   
## AWin_v_Neut_R_Ins_r2  |   0.79    |   0.03   | 7.21e-03  | -9.86e-03 |   -0.02   |   -0.46   |    1.61    |    0.22   
## BWin_v_Neut_R_Ins_r1  |   -0.01   |   0.62   |   0.02    |   -0.08   |   -0.75   |   -0.01   |    1.96    |  3.19e-03 
## BWin_v_Neut_R_Ins_r2  |   0.86    |  -0.04   |   -0.06   |   0.01    | 6.56e-03  |   -0.64   |    1.87    |  3.49e-03 
## ALose_v_Neut_L_Ins_r1 |   -0.03   |   0.57   | 1.19e-03  |   0.06    | 9.32e-03  |   -0.04   |    1.04    |    0.66   
## ALose_v_Neut_R_Ins_r1 | -7.34e-03 |   0.89   |   -0.01   |   -0.02   |   0.07    | -5.10e-04 |    1.01    |    0.23   
## ALose_v_Neut_L_Ins_r2 |   0.58    |   0.05   |   0.06    | 6.76e-03  |   -0.04   |   0.14    |    1.17    |    0.60   
## ALose_v_Neut_R_Ins_r2 |   0.89    | 4.13e-03 | 6.48e-03  |   -0.02   |   0.02    |   0.11    |    1.03    |    0.19   
## BLose_v_Neut_L_Ins_r1 | -9.55e-03 |   0.64   |   0.03    |   0.08    |   0.14    | 1.89e-03  |    1.13    |    0.58   
## BLose_v_Neut_R_Ins_r1 |   0.01    |   0.99   |   0.04    | 6.94e-04  |   0.31    |   0.03    |    1.20    |  3.66e-03 
## BLose_v_Neut_L_Ins_r2 |   0.65    |   0.04   |   0.07    |   -0.02   |   -0.03   |   0.27    |    1.38    |    0.46   
## BLose_v_Neut_R_Ins_r2 |   0.92    |  -0.02   |   0.02    |   -0.04   |   0.04    |   0.33    |    1.27    |  3.16e-03 
## BLose_v_BWin_L_Ins_r1 | 8.68e-03  |   0.24   | 4.34e-03  |   -0.02   |   0.66    |   -0.02   |    1.26    |    0.54   
## BLose_v_BWin_R_Ins_r1 |   0.02    |   0.25   |   0.01    |   0.08    |   1.03    |   0.04    |    1.14    |  3.22e-03 
## BLose_v_BWin_L_Ins_r2 |   0.14    |  -0.03   |   -0.10   |   0.07    | -6.14e-03 |   0.61    |    1.20    |    0.55   
## BLose_v_BWin_R_Ins_r2 |   0.17    |   0.02   |   0.09    |   -0.05   |   0.04    |   1.00    |    1.08    |  3.44e-03 
## 
## The 6 latent factors (Promax rotation) accounted for 65.06% of the total variance of the original data (ML1 = 13.88%, ML4 = 12.36%, ML6 = 11.22%, ML5 = 10.79%, ML2 = 9.01%, ML3 = 7.79%).

# factor corr
factor_corr_abcd = abcd_efa$Phi
colnames(factor_corr_abcd) = paste(1:abcd_efa$factors)
rownames(factor_corr_abcd) = paste("AD",1:abcd_efa$factors)
factor_corr_abcd

##                1          2           3           4           5           6
## AD 1  1.00000000  0.1602985  0.11413610  0.07469508 -0.14575376  0.09393775
## AD 2  0.16029849  1.0000000 -0.14756070  0.15926040 -0.13075325  0.06844910
## AD 3  0.11413610 -0.1475607  1.00000000  0.26813426 -0.04624448 -0.28406597
## AD 4  0.07469508  0.1592604  0.26813426  1.00000000 -0.33952930  0.04554245
## AD 5 -0.14575376 -0.1307532 -0.04624448 -0.33952930  1.00000000 -0.15700011
## AD 6  0.09393775  0.0684491 -0.28406597  0.04554245 -0.15700011  1.00000000

corrplot(factor_corr_abcd, method = "color", is.corr = TRUE, 
         number.digits = 3,addCoef.col = "black",number.cex = .7,
         tl.cex = .8, tl.col = "black", type = "lower")

remove loadings <20

# dont print values below .20
abcd_loadings_thresh <- abcd_efa$loadings[, 1:abcd_factors]
abcd_loadings_thresh[abs(abcd_loadings_thresh) < .20] <- NA
rownames(abcd_loadings_thresh) <- efa_rownames

heatmaply(round(abcd_loadings_thresh,2) %>% print(sort = T),
          colors = c("#ca0000","white","#3182bd"),
          
           dendrogram = "none",
           xlab = "", ylab = "", 
           main = "",
           margins = c(60,100,40,20),
           grid_color = "white",
           grid_width = 0.00001,
           titleX = FALSE,
           hide_colorbar = FALSE,
           branches_lwd = 0.1,
           fontsize_row = 14, fontsize_col = 14,
           labCol = colnames(abcd_loadings_thresh),
           labRow = rownames(abcd_loadings_thresh),
           heatmap_layers = theme(axis.line=element_blank()),
          
)

##                                  AD 1 AD 2 AD 3 AD 4  AD 5  AD 6
## 1. R1: All Win > $0 L-NAc          NA   NA   NA 0.60    NA    NA
## 2. R1: All Win > $0 R-NAc          NA   NA   NA 0.97    NA    NA
## 3. R2: All Win > $0 L-NAc          NA   NA 0.94   NA    NA    NA
## 4. R2: All Win > $0 R-NAc          NA   NA 0.66   NA    NA    NA
## 5. R1: Big Win > $0 L-NAc          NA   NA   NA 0.63    NA    NA
## 6. R1: Big Win > $0 R-NAc          NA   NA   NA 0.99    NA    NA
## 7. R2: Big Win > $0 L-NAc          NA   NA 0.99   NA    NA    NA
## 8. R2: Big Win > $0 R-NAc          NA   NA 0.67   NA    NA    NA
## 9. R1: Big Win > Big Lose L-NAc    NA   NA   NA 0.29 -0.27    NA
## 10. R1: Big Win > Big Lose R-NAc   NA   NA   NA 0.52    NA    NA
## 11. R2: Big Win > Big Lose L-NAc   NA   NA 0.50   NA    NA    NA
## 12. R2: Big Win > Big Lose R-NAc   NA   NA 0.38   NA    NA    NA
## 13. R1: All Win > $0 R-Ins         NA 0.64   NA   NA -0.57    NA
## 14. R2: All Win > $0 R-Ins       0.79   NA   NA   NA    NA -0.46
## 15. R1: Big Win > $0 R-Ins         NA 0.62   NA   NA -0.75    NA
## 16. R2: Big Win > $0 R-Ins       0.86   NA   NA   NA    NA -0.64
## 17. R1: All Lose > $0 L-Ins        NA 0.57   NA   NA    NA    NA
## 18. R1: All Lose > $0 R-Ins        NA 0.89   NA   NA    NA    NA
## 19. R2: All Lose > $0 L-Ins      0.58   NA   NA   NA    NA    NA
## 20. R2: All Lose > $0 R-Ins      0.89   NA   NA   NA    NA    NA
## 21. R1: Big Lose > $0 L-Ins        NA 0.64   NA   NA    NA    NA
## 22. R1: Big Lose > $0 R-Ins        NA 0.99   NA   NA  0.31    NA
## 23. R2: Big Lose > $0 L-Ins      0.65   NA   NA   NA    NA  0.27
## 24. R2: Big Lose > $0 R-Ins      0.92   NA   NA   NA    NA  0.33
## 25. R1: Big Lose > Big Win L-Ins   NA 0.24   NA   NA  0.66    NA
## 26. R1: Big Lose > Big Win R-Ins   NA 0.25   NA   NA  1.03    NA
## 27. R2: Big Lose > Big Win L-Ins   NA   NA   NA   NA    NA  0.61
## 28. R2: Big Lose > Big Win R-Ins   NA   NA   NA   NA    NA  1.00

7.2.2 AHRB EFA

ahrb_factors = 6

ahrb_efa = fa(ahrb_df[,mod_vars], nfactors = ahrb_factors,
              rotate = 'Promax', fm = 'ml')

ahrb_colnames = paste0("AB", 1:ahrb_efa$factors)

colnames(ahrb_efa$loadings) <- paste("AB", 1:abcd_efa$factors)

# extract correlation matrix of residuals?
model_parameters(ahrb_efa)

## # Rotated loadings from Factor Analysis (Promax-rotation)
## 
## Variable              |   AB 1    |   AB 2    |   AB 3    |   AB 4    |   AB 5    |   AB 6    | Complexity | Uniqueness
## -----------------------------------------------------------------------------------------------------------------------
## AWin_v_Neut_L_NAc_r1  |   0.02    |   -0.07   |   0.44    |   -0.04   |   0.02    |   0.07    |    1.13    |    0.81   
## AWin_v_Neut_R_NAc_r1  |   0.04    | -3.22e-03 |   0.84    |   -0.02   | -5.68e-05 |   0.06    |    1.02    |    0.29   
## AWin_v_Neut_L_NAc_r2  | -7.51e-03 |   -0.07   |   -0.03   |   0.95    |   0.04    |   -0.08   |    1.03    |    0.16   
## AWin_v_Neut_R_NAc_r2  |   -0.02   |   0.13    |   -0.10   |   0.39    |   -0.21   |   0.11    |    2.16    |    0.69   
## BWin_v_Neut_L_NAc_r1  |   0.05    | 8.86e-04  |   0.52    |   0.05    |   -0.01   |   0.02    |    1.04    |    0.71   
## BWin_v_Neut_R_NAc_r1  |   0.02    |   0.06    |   1.00    |   0.01    |   0.05    | 5.55e-03  |    1.01    |  5.00e-03 
## BWin_v_Neut_L_NAc_r2  |   0.07    |   -0.05   |   0.02    |   1.02    |   0.18    |   -0.08   |    1.09    |    0.07   
## BWin_v_Neut_R_NAc_r2  |   0.03    |   0.09    |   -0.04   |   0.54    |   -0.20   |   0.15    |    1.53    |    0.54   
## BWin_v_BLose_L_NAc_r1 |   0.07    |   -0.06   |   0.26    |   -0.04   |   -0.14   |   -0.14   |    2.48    |    0.86   
## BWin_v_BLose_R_NAc_r1 | 6.48e-03  |   0.13    |   0.56    |   -0.05   |   -0.03   |   -0.03   |    1.14    |    0.65   
## BWin_v_BLose_L_NAc_r2 |   -0.06   |   0.07    |   0.16    |   0.50    |   0.04    | 2.36e-03  |    1.31    |    0.70   
## BWin_v_BLose_R_NAc_r2 |   -0.04   |   0.08    |   0.07    |   0.20    |   -0.18   |   0.10    |    3.16    |    0.87   
## AWin_v_Neut_R_Ins_r1  |   0.88    |   0.02    | 9.67e-03  |   0.08    | 2.43e-03  |   -0.21   |    1.14    |    0.21   
## AWin_v_Neut_R_Ins_r2  |   -0.08   |   0.78    |   0.08    |   -0.15   |   -0.41   |   -0.03   |    1.66    |    0.16   
## BWin_v_Neut_R_Ins_r1  |   0.92    |   -0.01   | -2.04e-03 |   0.04    |   -0.01   |   -0.50   |    1.55    |  3.37e-03 
## BWin_v_Neut_R_Ins_r2  |   -0.05   |   0.79    | 2.75e-04  |   -0.07   |   -0.50   |   -0.03   |    1.73    |  3.14e-03 
## ALose_v_Neut_L_Ins_r1 |   0.61    |   0.01    |   -0.02   |   -0.05   |   -0.06   |   0.07    |    1.06    |    0.60   
## ALose_v_Neut_R_Ins_r1 |   0.90    |   -0.05   |   0.07    |   0.05    |   0.08    |   0.16    |    1.11    |    0.14   
## ALose_v_Neut_L_Ins_r2 |   0.13    |   0.59    |   -0.08   |   -0.03   |   0.10    |   0.03    |    1.21    |    0.63   
## ALose_v_Neut_R_Ins_r2 |   -0.01   |   0.92    |   0.07    | -9.00e-03 |   0.16    |   0.06    |    1.08    |    0.20   
## BLose_v_Neut_L_Ins_r1 |   0.61    |   -0.04   |   -0.11   |   -0.08   |   -0.13   |   0.19    |    1.41    |    0.55   
## BLose_v_Neut_R_Ins_r1 |   0.89    | 6.79e-03  |   0.03    |   -0.04   |   0.04    |   0.35    |    1.31    |  3.10e-03 
## BLose_v_Neut_L_Ins_r2 |   0.09    |   0.64    |   -0.15   | 9.75e-03  |   0.19    |   -0.04   |    1.33    |    0.55   
## BLose_v_Neut_R_Ins_r2 | -7.01e-03 |   1.01    |   0.03    |   0.03    |   0.38    | -5.27e-04 |    1.28    |  3.24e-03 
## BLose_v_BWin_L_Ins_r1 |   0.06    |   -0.08   |   -0.04   |   -0.02   |   -0.02   |   0.59    |    1.07    |    0.62   
## BLose_v_BWin_R_Ins_r1 |   0.06    |   0.02    |   0.04    |   -0.09   |   0.07    |   0.99    |    1.04    |  3.66e-03 
## BLose_v_BWin_L_Ins_r2 |   -0.06   |   0.10    |   0.06    |   -0.06   |   0.73    |   0.06    |    1.09    |    0.46   
## BLose_v_BWin_R_Ins_r2 |   0.05    |   0.23    |   0.03    |   0.12    |   1.06    |   0.04    |    1.13    |  3.72e-03 
## 
## The 6 latent factors (Promax rotation) accounted for 62.52% of the total variance of the original data (ML2 = 14.42%, ML3 = 14.01%, ML5 = 9.48%, ML6 = 9.43%, ML1 = 8.37%, ML4 = 6.81%).

# factor corr
factor_corr_ahrb = ahrb_efa$Phi
colnames(factor_corr_ahrb) = paste(1:ahrb_efa$factors)
rownames(factor_corr_ahrb) = paste("AB",1:ahrb_efa$factors)
factor_corr_ahrb

##                 1           2           3            4           5           6
## AB 1  1.000000000  0.18957317  0.19033633  0.001036987 -0.13380988  0.10826702
## AB 2  0.189573173  1.00000000  0.04923718  0.306680898 -0.22445819 -0.11140703
## AB 3  0.190336331  0.04923718  1.00000000  0.108018730 -0.22726451 -0.13092554
## AB 4  0.001036987  0.30668090  0.10801873  1.000000000 -0.35499055 -0.01888446
## AB 5 -0.133809885 -0.22445819 -0.22726451 -0.354990546  1.00000000  0.06046738
## AB 6  0.108267022 -0.11140703 -0.13092554 -0.018884457  0.06046738  1.00000000

corrplot(factor_corr_ahrb, method = "color", is.corr = TRUE, 
         number.digits = 3,addCoef.col = "black",number.cex = .7,
         tl.cex = .8, tl.col = "black", type = "lower")

remove <.20 loadings and reorder to match ABCD order

# reorder factors to maps ABCD order:
ahrb_efa_loadings_rev <- ahrb_efa$loadings[,c(2,1,4,3,5,6)]

# dont print values below .20
ahrb_loadings_thresh <- ahrb_efa_loadings_rev[, 1:ahrb_factors]
ahrb_loadings_thresh[abs(ahrb_loadings_thresh) < .30] <- NA

rownames(ahrb_loadings_thresh) <- efa_rownames

heatmaply(round(ahrb_loadings_thresh,2) %>% print(sort = T),
          colors = c("#ca0000","white","#3182bd"),
               dendrogram = "none",
               xlab = "", ylab = "", 
               main = "",
               margins = c(60,100,40,20),
               grid_color = "white",
               grid_width = 0.00001,
               titleX = FALSE,
               hide_colorbar = FALSE,
               branches_lwd = 0.1,
               label_names = c("Brain:", "Feature:", "Value"),
               fontsize_row = 14, fontsize_col = 14,
               labCol = colnames(ahrb_loadings_thresh),
               labRow = rownames(ahrb_loadings_thresh),
               heatmap_layers = theme(axis.line=element_blank()),
          
)

##                                  AB 2 AB 1 AB 4 AB 3  AB 5  AB 6
## 1. R1: All Win > $0 L-NAc          NA   NA   NA 0.44    NA    NA
## 2. R1: All Win > $0 R-NAc          NA   NA   NA 0.84    NA    NA
## 3. R2: All Win > $0 L-NAc          NA   NA 0.95   NA    NA    NA
## 4. R2: All Win > $0 R-NAc          NA   NA 0.39   NA    NA    NA
## 5. R1: Big Win > $0 L-NAc          NA   NA   NA 0.52    NA    NA
## 6. R1: Big Win > $0 R-NAc          NA   NA   NA 1.00    NA    NA
## 7. R2: Big Win > $0 L-NAc          NA   NA 1.02   NA    NA    NA
## 8. R2: Big Win > $0 R-NAc          NA   NA 0.54   NA    NA    NA
## 9. R1: Big Win > Big Lose L-NAc    NA   NA   NA   NA    NA    NA
## 10. R1: Big Win > Big Lose R-NAc   NA   NA   NA 0.56    NA    NA
## 11. R2: Big Win > Big Lose L-NAc   NA   NA 0.50   NA    NA    NA
## 12. R2: Big Win > Big Lose R-NAc   NA   NA   NA   NA    NA    NA
## 13. R1: All Win > $0 R-Ins         NA 0.88   NA   NA    NA    NA
## 14. R2: All Win > $0 R-Ins       0.78   NA   NA   NA -0.41    NA
## 15. R1: Big Win > $0 R-Ins         NA 0.92   NA   NA    NA -0.50
## 16. R2: Big Win > $0 R-Ins       0.79   NA   NA   NA -0.50    NA
## 17. R1: All Lose > $0 L-Ins        NA 0.61   NA   NA    NA    NA
## 18. R1: All Lose > $0 R-Ins        NA 0.90   NA   NA    NA    NA
## 19. R2: All Lose > $0 L-Ins      0.59   NA   NA   NA    NA    NA
## 20. R2: All Lose > $0 R-Ins      0.92   NA   NA   NA    NA    NA
## 21. R1: Big Lose > $0 L-Ins        NA 0.61   NA   NA    NA    NA
## 22. R1: Big Lose > $0 R-Ins        NA 0.89   NA   NA    NA  0.35
## 23. R2: Big Lose > $0 L-Ins      0.64   NA   NA   NA    NA    NA
## 24. R2: Big Lose > $0 R-Ins      1.01   NA   NA   NA  0.38    NA
## 25. R1: Big Lose > Big Win L-Ins   NA   NA   NA   NA    NA  0.59
## 26. R1: Big Lose > Big Win R-Ins   NA   NA   NA   NA    NA  0.99
## 27. R2: Big Lose > Big Win L-Ins   NA   NA   NA   NA  0.73    NA
## 28. R2: Big Lose > Big Win R-Ins   NA   NA   NA   NA  1.06    NA

7.2.3 MLS EFA

mls_factors = 7

mls_efa = fa(mls_df[,mod_vars], nfactors = mls_factors,
              rotate = 'Promax', fm = 'ml')

mls_colnames = paste0("MS", 1:mls_efa$factors)

colnames(mls_efa$loadings) <- mls_colnames
model_parameters(mls_efa)

## # Rotated loadings from Factor Analysis (Promax-rotation)
## 
## Variable              |    MS1    |   MS2    |    MS3    |    MS4    |    MS5    |   MS6    |    MS7    | Complexity | Uniqueness
## ---------------------------------------------------------------------------------------------------------------------------------
## AWin_v_Neut_L_NAc_r1  |   0.93    |   0.07   |   -0.05   | 6.23e-03  |   0.03    |   0.07   |   -0.03   |    1.03    |    0.14   
## AWin_v_Neut_R_NAc_r1  |   0.61    |   0.06   |   -0.01   |   -0.02   | -2.91e-03 |   0.03   |   0.06    |    1.04    |    0.60   
## AWin_v_Neut_L_NAc_r2  |   0.03    |   0.96   |   0.04    | 1.87e-03  |   0.07    |  -0.12   |   0.02    |    1.05    |    0.13   
## AWin_v_Neut_R_NAc_r2  |   -0.08   |   0.66   |   0.05    |   0.07    | 8.27e-03  |   0.04   | 3.86e-04  |    1.07    |    0.53   
## BWin_v_Neut_L_NAc_r1  |   0.97    |   0.08   |   -0.04   |   0.01    |   0.04    |   0.09   |   -0.02   |    1.04    |    0.03   
## BWin_v_Neut_R_NAc_r1  |   0.70    |   0.03   |   -0.03   |   0.02    |   -0.03   |   0.03   |   0.07    |    1.04    |    0.48   
## BWin_v_Neut_L_NAc_r2  |   0.13    |   0.95   |   0.03    |   0.03    |   0.05    |  -0.05   | 4.00e-03  |    1.06    |    0.08   
## BWin_v_Neut_R_NAc_r2  |   -0.01   |   0.69   |   -0.07   |   0.13    |   -0.01   |   0.10   | -2.72e-03 |    1.14    |    0.45   
## BWin_v_BLose_L_NAc_r1 |   0.65    |  -0.07   |   0.02    |   0.04    | 1.24e-03  |  -0.07   |   -0.01   |    1.06    |    0.57   
## BWin_v_BLose_R_NAc_r1 |   0.48    |  -0.15   |   0.07    |   0.04    |   -0.07   |  -0.12   |   0.03    |    1.46    |    0.73   
## BWin_v_BLose_L_NAc_r2 |   0.12    |   0.45   |   -0.05   |   -0.22   |   -0.09   |  -0.02   |   -0.11   |    1.90    |    0.75   
## BWin_v_BLose_R_NAc_r2 |   -0.07   |   0.31   |   -0.02   |   -0.20   |   -0.06   |   0.10   |   -0.01   |    2.22    |    0.86   
## AWin_v_Neut_R_Ins_r1  |   -0.05   |  -0.04   |   0.89    |   -0.03   |   -0.02   |   0.04   |   -0.21   |    1.12    |    0.22   
## AWin_v_Neut_R_Ins_r2  |   -0.11   |  -0.04   |   -0.01   |   0.41    |   -0.69   | 1.33e-03 |   0.04    |    1.68    |    0.23   
## BWin_v_Neut_R_Ins_r1  |   -0.05   |   0.06   |   0.96    | -2.54e-03 | -6.31e-03 |   0.07   |   -0.35   |    1.29    |  3.45e-03 
## BWin_v_Neut_R_Ins_r2  |   -0.02   |  -0.04   |   -0.02   |   0.42    |   -0.81   |   0.03   |   -0.03   |    1.52    |  3.12e-03 
## ALose_v_Neut_L_Ins_r1 |   0.13    |  -0.06   |   0.12    | -8.50e-03 | -8.37e-03 |   0.95   |   -0.17   |    1.15    |    0.15   
## ALose_v_Neut_R_Ins_r1 |   0.01    |   0.03   |   0.71    | -3.31e-03 |   0.03    |   0.07   |   0.33    |    1.43    |    0.23   
## ALose_v_Neut_L_Ins_r2 | 9.46e-03  |   0.08   |   0.09    |   0.32    |   -0.03   |  -0.06   |   -0.05   |    1.46    |    0.85   
## ALose_v_Neut_R_Ins_r2 |   0.12    |   0.04   |   0.04    |   0.79    |   -0.03   |  -0.04   |   -0.03   |    1.07    |    0.30   
## BLose_v_Neut_L_Ins_r1 |   0.09    |  -0.10   |   0.10    | 5.20e-03  |   -0.03   |   0.97   |   -0.02   |    1.06    |  4.98e-03 
## BLose_v_Neut_R_Ins_r1 |   -0.05   |   0.05   |   0.69    |   -0.02   |   0.02    | 2.80e-03 |   0.62    |    2.01    |  3.13e-03 
## BLose_v_Neut_L_Ins_r2 |   -0.08   |   0.02   |   0.02    |   0.39    |   0.05    |   0.03   |   -0.08   |    1.22    |    0.84   
## BLose_v_Neut_R_Ins_r2 |   -0.01   |   0.04   |   -0.04   |   1.04    |   0.18    |   0.02   | -7.68e-04 |    1.07    |  3.60e-03 
## BLose_v_BWin_L_Ins_r1 |   -0.08   | 2.69e-03 |   -0.25   |   0.05    | -5.56e-03 |   0.56   |   0.37    |    2.23    |    0.40   
## BLose_v_BWin_R_Ins_r1 | -6.65e-03 | 2.58e-03 |   -0.20   |   -0.02   |   0.03    |  -0.06   |   1.03    |    1.09    |  3.43e-03 
## BLose_v_BWin_L_Ins_r2 |   -0.05   |  -0.15   | -8.12e-03 |   0.06    |   0.43    |   0.07   |   -0.10   |    1.49    |    0.76   
## BLose_v_BWin_R_Ins_r2 |   0.01    |   0.08   |   -0.02   |   0.51    |   1.02    |  -0.02   |   0.03    |    1.48    |  3.31e-03 
## 
## The 7 latent factors (Promax rotation) accounted for 66.56% of the total variance of the original data (ML6 = 12.33%, ML7 = 11.05%, ML1 = 10.40%, ML2 = 9.45%, ML3 = 8.44%, ML5 = 8.16%, ML4 = 6.73%).

# factor corr
factor_corr_mls = mls_efa$Phi
colnames(factor_corr_mls) = paste(c("4","3","2","1","5","7","6"))
rownames(factor_corr_mls) = paste(c("MS 4","MS 3","MS 2","MS 1","MS 5","MS 7","MS 6"))
factor_corr_mls

##                 4          3          2           1            5            7
## MS 4  1.000000000  0.1023792 0.08203506  0.10920647  0.002485229 -0.001581897
## MS 3  0.102379193  1.0000000 0.14519935  0.18705140 -0.282196393  0.194144994
## MS 2  0.082035057  0.1451994 1.00000000  0.28869446  0.005460810  0.393577136
## MS 1  0.109206470  0.1870514 0.28869446  1.00000000 -0.270848500  0.137674656
## MS 5  0.002485229 -0.2821964 0.00546081 -0.27084850  1.000000000 -0.029588148
## MS 7 -0.001581897  0.1941450 0.39357714  0.13767466 -0.029588148  1.000000000
## MS 6  0.184823061  0.1375838 0.14314572 -0.02193652  0.053117731  0.519076338
##                6
## MS 4  0.18482306
## MS 3  0.13758377
## MS 2  0.14314572
## MS 1 -0.02193652
## MS 5  0.05311773
## MS 7  0.51907634
## MS 6  1.00000000

corrplot(factor_corr_mls, method = "color", is.corr = TRUE, 
         number.digits = 3,addCoef.col = "black",number.cex = .7,
         tl.cex = .8, tl.col = "black", type = "lower")

remove <.20 loadings and reorder to match ABCD order

# reorder factors to maps ABCD order:
mls_efa_loadings_rev <- mls_efa$loadings[,c(4,3,2,1,5,7,6)]
# dont print values below .20
mls_loadings_thresh <- mls_efa_loadings_rev[, 1:mls_factors]
mls_loadings_thresh[abs(mls_loadings_thresh) < .30] <- NA

rownames(mls_loadings_thresh) <- efa_rownames

heatmaply(round(mls_loadings_thresh,2) %>% print(sort = T),
         #scale_fill_gradient_fun = ggplot2::scale_fill_gradient2(
         #       low = "darkred", 
         #       high = "blue",
         #       space = "Lab",
         #       midpoint = 0, 
         #       limits = c(-1, 1)
         #     ),
         
          colors = c("#ca0000","white","#3182bd"),
               dendrogram = "none",
               xlab = "", ylab = "", 
               main = "",
               margins = c(60,100,40,20),
               grid_color = "white",
               grid_width = 0.00001,
               titleX = FALSE,
               hide_colorbar = FALSE,
               branches_lwd = 0.1,
               label_names = c("Brain:", "Feature:", "Value"),
               fontsize_row = 14, fontsize_col = 14,
               col_names = colnames(mls_loadings_thresh),
               labRow = rownames(mls_loadings_thresh),
               heatmap_layers = theme(axis.line=element_blank())
) 

##                                   MS4  MS3  MS2  MS1   MS5   MS7  MS6
## 1. R1: All Win > $0 L-NAc          NA   NA   NA 0.93    NA    NA   NA
## 2. R1: All Win > $0 R-NAc          NA   NA   NA 0.61    NA    NA   NA
## 3. R2: All Win > $0 L-NAc          NA   NA 0.96   NA    NA    NA   NA
## 4. R2: All Win > $0 R-NAc          NA   NA 0.66   NA    NA    NA   NA
## 5. R1: Big Win > $0 L-NAc          NA   NA   NA 0.97    NA    NA   NA
## 6. R1: Big Win > $0 R-NAc          NA   NA   NA 0.70    NA    NA   NA
## 7. R2: Big Win > $0 L-NAc          NA   NA 0.95   NA    NA    NA   NA
## 8. R2: Big Win > $0 R-NAc          NA   NA 0.69   NA    NA    NA   NA
## 9. R1: Big Win > Big Lose L-NAc    NA   NA   NA 0.65    NA    NA   NA
## 10. R1: Big Win > Big Lose R-NAc   NA   NA   NA 0.48    NA    NA   NA
## 11. R2: Big Win > Big Lose L-NAc   NA   NA 0.45   NA    NA    NA   NA
## 12. R2: Big Win > Big Lose R-NAc   NA   NA 0.31   NA    NA    NA   NA
## 13. R1: All Win > $0 R-Ins         NA 0.89   NA   NA    NA    NA   NA
## 14. R2: All Win > $0 R-Ins       0.41   NA   NA   NA -0.69    NA   NA
## 15. R1: Big Win > $0 R-Ins         NA 0.96   NA   NA    NA -0.35   NA
## 16. R2: Big Win > $0 R-Ins       0.42   NA   NA   NA -0.81    NA   NA
## 17. R1: All Lose > $0 L-Ins        NA   NA   NA   NA    NA    NA 0.95
## 18. R1: All Lose > $0 R-Ins        NA 0.71   NA   NA    NA  0.33   NA
## 19. R2: All Lose > $0 L-Ins      0.32   NA   NA   NA    NA    NA   NA
## 20. R2: All Lose > $0 R-Ins      0.79   NA   NA   NA    NA    NA   NA
## 21. R1: Big Lose > $0 L-Ins        NA   NA   NA   NA    NA    NA 0.97
## 22. R1: Big Lose > $0 R-Ins        NA 0.69   NA   NA    NA  0.62   NA
## 23. R2: Big Lose > $0 L-Ins      0.39   NA   NA   NA    NA    NA   NA
## 24. R2: Big Lose > $0 R-Ins      1.04   NA   NA   NA    NA    NA   NA
## 25. R1: Big Lose > Big Win L-Ins   NA   NA   NA   NA    NA  0.37 0.56
## 26. R1: Big Lose > Big Win R-Ins   NA   NA   NA   NA    NA  1.03   NA
## 27. R2: Big Lose > Big Win L-Ins   NA   NA   NA   NA  0.43    NA   NA
## 28. R2: Big Lose > Big Win R-Ins 0.51   NA   NA   NA  1.02    NA   NA

7.3 Factor Congruence

Calculating a coefficient of factor congruence across the three samples’ EFA models. Using function fa.congruence

abcd_revised <- c("AD1","AD2","AD3","AD4","AD5","AD6")
fa_cong_table = fa.congruence(x = list(abcd_efa,ahrb_efa,mls_efa), digits = 2) 

# rename rows/columns to improve interpretability

colnames(fa_cong_table) <- c(abcd_revised,ahrb_colnames,mls_colnames)
rownames(fa_cong_table) <- c(abcd_revised,ahrb_colnames,mls_colnames)
fa_cong_table %>% 
  knitr::kable(
    caption = "Factor Congruence: ABCD, AHRB & MLS EFA",
    booktabs = TRUE
    )

Factor Congruence: ABCD, AHRB & MLS EFA

	AD1	AD2	AD3	AD4	AD5	AD6	AB1	AB2	AB3	AB4	AB5	AB6	MS1	MS2	MS3	MS4	MS5	MS6	MS7
AD1	1.00	0.00	0.01	-0.03	0.02	0.02	-0.01	0.97	-0.03	-0.06	0.06	0.02	-0.04	0.02	0.00	0.92	-0.27	-0.01	-0.02
AD2	0.00	1.00	0.02	-0.01	0.03	0.01	0.96	-0.02	-0.01	0.00	0.03	0.23	0.00	0.01	0.79	-0.01	0.02	0.51	0.30
AD3	0.01	0.02	1.00	-0.01	0.01	0.06	0.03	0.05	0.02	0.96	-0.02	0.03	0.10	0.98	0.02	0.03	0.05	-0.01	-0.01
AD4	-0.03	-0.01	-0.01	1.00	0.07	-0.03	0.02	-0.01	0.95	-0.05	-0.01	0.08	0.89	-0.01	-0.06	0.00	-0.02	0.07	0.09
AD5	0.02	0.03	0.01	0.07	1.00	0.03	-0.21	-0.01	0.01	-0.06	0.06	0.94	-0.03	0.03	-0.49	0.02	0.04	0.17	0.85
AD6	0.02	0.01	0.06	-0.03	0.03	1.00	0.04	0.04	-0.04	0.11	0.95	0.06	-0.01	0.04	0.01	0.29	0.94	-0.03	0.01
AB1	-0.01	0.96	0.03	0.02	-0.21	0.04	1.00	-0.01	0.03	0.03	0.03	0.02	0.05	0.01	0.90	0.00	0.04	0.45	0.11
AB2	0.97	-0.02	0.05	-0.01	-0.01	0.04	-0.01	1.00	0.03	-0.03	0.08	0.01	-0.02	0.04	0.00	0.91	-0.24	-0.02	-0.04
AB3	-0.03	-0.01	0.02	0.95	0.01	-0.04	0.03	0.03	1.00	0.00	0.03	0.03	0.85	0.01	0.00	0.01	-0.02	-0.04	0.08
AB4	-0.06	0.00	0.96	-0.05	-0.06	0.11	0.03	-0.03	0.00	1.00	0.09	-0.07	0.04	0.97	0.05	-0.01	0.13	-0.08	-0.07
AB5	0.06	0.03	-0.02	-0.01	0.06	0.95	0.03	0.08	0.03	0.09	1.00	0.05	0.00	-0.01	0.02	0.31	0.89	-0.09	0.03
AB6	0.02	0.23	0.03	0.08	0.94	0.06	0.02	0.01	0.03	-0.07	0.05	1.00	0.00	0.03	-0.28	0.02	0.06	0.26	0.89
MS1	-0.04	0.00	0.10	0.89	-0.03	-0.01	0.05	-0.02	0.85	0.04	0.00	0.00	1.00	0.06	-0.04	0.01	0.03	0.08	-0.01
MS2	0.02	0.01	0.98	-0.01	0.03	0.04	0.01	0.04	0.01	0.97	-0.01	0.03	0.06	1.00	0.03	0.04	0.05	-0.07	0.01
MS3	0.00	0.79	0.02	-0.06	-0.49	0.01	0.90	0.00	0.00	0.05	0.02	-0.28	-0.04	0.03	1.00	-0.02	0.00	0.08	-0.08
MS4	0.92	-0.01	0.03	0.00	0.02	0.29	0.00	0.91	0.01	-0.01	0.31	0.02	0.01	0.04	-0.02	1.00	0.05	0.01	-0.01
MS5	-0.27	0.02	0.05	-0.02	0.04	0.94	0.04	-0.24	-0.02	0.13	0.89	0.06	0.03	0.05	0.00	0.05	1.00	-0.02	0.02
MS6	-0.01	0.51	-0.01	0.07	0.17	-0.03	0.45	-0.02	-0.04	-0.08	-0.09	0.26	0.08	-0.07	0.08	0.01	-0.02	1.00	-0.03
MS7	-0.02	0.30	-0.01	0.09	0.85	0.01	0.11	-0.04	0.08	-0.07	0.03	0.89	-0.01	0.01	-0.08	-0.01	0.02	-0.03	1.00

corrplot(fa_cong_table, method = "color", tl.cex = .8, type = "lower")

# relabeled MS1 = MS4 | MS2 = AD3 | MS3 = AD2 | MS4 = AD1 | MS5 = AD6 | MS6 = AD2

ahrb_revised <- c("AB2","AB1","AB4","AB3","AB5","AB6")
mls_revised <- c("MS4","MS3","MS2","MS1","MS6","MS5","MS7")
colnames(fa_cong_table) <- c(abcd_revised,ahrb_revised,mls_revised)
rownames(fa_cong_table) <- c(abcd_revised,ahrb_revised,mls_revised)
fa_cong_table %>% 
  knitr::kable(
    caption = "Factor Congruence: ABCD, AHRB & MLS EFA",
    booktabs = TRUE
    )

Factor Congruence: ABCD, AHRB & MLS EFA

	AD1	AD2	AD3	AD4	AD5	AD6	AB2	AB1	AB4	AB3	AB5	AB6	MS4	MS3	MS2	MS1	MS6	MS5	MS7
AD1	1.00	0.00	0.01	-0.03	0.02	0.02	-0.01	0.97	-0.03	-0.06	0.06	0.02	-0.04	0.02	0.00	0.92	-0.27	-0.01	-0.02
AD2	0.00	1.00	0.02	-0.01	0.03	0.01	0.96	-0.02	-0.01	0.00	0.03	0.23	0.00	0.01	0.79	-0.01	0.02	0.51	0.30
AD3	0.01	0.02	1.00	-0.01	0.01	0.06	0.03	0.05	0.02	0.96	-0.02	0.03	0.10	0.98	0.02	0.03	0.05	-0.01	-0.01
AD4	-0.03	-0.01	-0.01	1.00	0.07	-0.03	0.02	-0.01	0.95	-0.05	-0.01	0.08	0.89	-0.01	-0.06	0.00	-0.02	0.07	0.09
AD5	0.02	0.03	0.01	0.07	1.00	0.03	-0.21	-0.01	0.01	-0.06	0.06	0.94	-0.03	0.03	-0.49	0.02	0.04	0.17	0.85
AD6	0.02	0.01	0.06	-0.03	0.03	1.00	0.04	0.04	-0.04	0.11	0.95	0.06	-0.01	0.04	0.01	0.29	0.94	-0.03	0.01
AB2	-0.01	0.96	0.03	0.02	-0.21	0.04	1.00	-0.01	0.03	0.03	0.03	0.02	0.05	0.01	0.90	0.00	0.04	0.45	0.11
AB1	0.97	-0.02	0.05	-0.01	-0.01	0.04	-0.01	1.00	0.03	-0.03	0.08	0.01	-0.02	0.04	0.00	0.91	-0.24	-0.02	-0.04
AB4	-0.03	-0.01	0.02	0.95	0.01	-0.04	0.03	0.03	1.00	0.00	0.03	0.03	0.85	0.01	0.00	0.01	-0.02	-0.04	0.08
AB3	-0.06	0.00	0.96	-0.05	-0.06	0.11	0.03	-0.03	0.00	1.00	0.09	-0.07	0.04	0.97	0.05	-0.01	0.13	-0.08	-0.07
AB5	0.06	0.03	-0.02	-0.01	0.06	0.95	0.03	0.08	0.03	0.09	1.00	0.05	0.00	-0.01	0.02	0.31	0.89	-0.09	0.03
AB6	0.02	0.23	0.03	0.08	0.94	0.06	0.02	0.01	0.03	-0.07	0.05	1.00	0.00	0.03	-0.28	0.02	0.06	0.26	0.89
MS4	-0.04	0.00	0.10	0.89	-0.03	-0.01	0.05	-0.02	0.85	0.04	0.00	0.00	1.00	0.06	-0.04	0.01	0.03	0.08	-0.01
MS3	0.02	0.01	0.98	-0.01	0.03	0.04	0.01	0.04	0.01	0.97	-0.01	0.03	0.06	1.00	0.03	0.04	0.05	-0.07	0.01
MS2	0.00	0.79	0.02	-0.06	-0.49	0.01	0.90	0.00	0.00	0.05	0.02	-0.28	-0.04	0.03	1.00	-0.02	0.00	0.08	-0.08
MS1	0.92	-0.01	0.03	0.00	0.02	0.29	0.00	0.91	0.01	-0.01	0.31	0.02	0.01	0.04	-0.02	1.00	0.05	0.01	-0.01
MS6	-0.27	0.02	0.05	-0.02	0.04	0.94	0.04	-0.24	-0.02	0.13	0.89	0.06	0.03	0.05	0.00	0.05	1.00	-0.02	0.02
MS5	-0.01	0.51	-0.01	0.07	0.17	-0.03	0.45	-0.02	-0.04	-0.08	-0.09	0.26	0.08	-0.07	0.08	0.01	-0.02	1.00	-0.03
MS7	-0.02	0.30	-0.01	0.09	0.85	0.01	0.11	-0.04	0.08	-0.07	0.03	0.89	-0.01	0.01	-0.08	-0.01	0.02	-0.03	1.00

corrplot(fa_cong_table, method = "color", tl.cex = .8, type = "lower")

8 Local SEM

Running CFA for the pubertal variables in the ABCD sample using the local SEM framework described in Olaru et al (2020) implemented using the sirt package

8.1 Specify Models

Specifying the model for the ABCD data below. Apply the EFA CFA from first n = 1000 ABCD sample in the held out second n = 1000 ABCD sample. Vary across Pubertal Developmental Scale. Use a parsiomnious model (e.g., FA loadings > .30). Again, fixing parameters exceeding ~ .85. Also, specifying theoretically plausible correlated residuals: within run + region similar signal

abcd_efa_residuals <- cor(data.frame(round(abcd_efa$residual,4)))
abcd_efa_residuals[abs(abcd_efa_residuals) < 0.60] <- 0

# plot/print matrix
as.matrix(abcd_efa_residuals) %>% 
  knitr::kable(
    caption = "First1k: ABCD Residuals Cov Matrix",
    booktabs = TRUE
    )

First1k: ABCD Residuals Cov Matrix

	AWin_v_Neut_L_NAc_r1	AWin_v_Neut_R_NAc_r1	AWin_v_Neut_L_NAc_r2	AWin_v_Neut_R_NAc_r2	BWin_v_Neut_L_NAc_r1	BWin_v_Neut_R_NAc_r1	BWin_v_Neut_L_NAc_r2	BWin_v_Neut_R_NAc_r2	BWin_v_BLose_L_NAc_r1	BWin_v_BLose_R_NAc_r1	BWin_v_BLose_L_NAc_r2	BWin_v_BLose_R_NAc_r2	AWin_v_Neut_R_Ins_r1	AWin_v_Neut_R_Ins_r2	BWin_v_Neut_R_Ins_r1	BWin_v_Neut_R_Ins_r2	ALose_v_Neut_L_Ins_r1	ALose_v_Neut_R_Ins_r1	ALose_v_Neut_L_Ins_r2	ALose_v_Neut_R_Ins_r2	BLose_v_Neut_L_Ins_r1	BLose_v_Neut_R_Ins_r1	BLose_v_Neut_L_Ins_r2	BLose_v_Neut_R_Ins_r2	BLose_v_BWin_L_Ins_r1	BLose_v_BWin_R_Ins_r1	BLose_v_BWin_L_Ins_r2	BLose_v_BWin_R_Ins_r2
AWin_v_Neut_L_NAc_r1	1.0000000	0.0000000	0.0000000	0.0000000	0.9399695	-0.6327199	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
AWin_v_Neut_R_NAc_r1	0.0000000	1.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	-0.6043899	-0.6164743	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
AWin_v_Neut_L_NAc_r2	0.0000000	0.0000000	1.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	-0.7304869	-0.7294328	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
AWin_v_Neut_R_NAc_r2	0.0000000	0.0000000	0.0000000	1.0000000	0.0000000	0.0000000	-0.6365843	0.9208651	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
BWin_v_Neut_L_NAc_r1	0.9399695	0.0000000	0.0000000	0.0000000	1.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
BWin_v_Neut_R_NAc_r1	-0.6327199	0.0000000	0.0000000	0.0000000	0.0000000	1.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
BWin_v_Neut_L_NAc_r2	0.0000000	0.0000000	0.0000000	-0.6365843	0.0000000	0.0000000	1.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
BWin_v_Neut_R_NAc_r2	0.0000000	0.0000000	0.0000000	0.9208651	0.0000000	0.0000000	0.0000000	1.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
BWin_v_BLose_L_NAc_r1	0.0000000	-0.6043899	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	1.0000000	0.7197583	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
BWin_v_BLose_R_NAc_r1	0.0000000	-0.6164743	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.7197583	1.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
BWin_v_BLose_L_NAc_r2	0.0000000	0.0000000	-0.7304869	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	1.0000000	0.7108924	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
BWin_v_BLose_R_NAc_r2	0.0000000	0.0000000	-0.7294328	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.7108924	1.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
AWin_v_Neut_R_Ins_r1	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	1	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
AWin_v_Neut_R_Ins_r2	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	1	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
BWin_v_Neut_R_Ins_r1	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	1.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.6712021	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
BWin_v_Neut_R_Ins_r2	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	1.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.7695138	0.0000000	0.000000	0.0000000	0.0000000
ALose_v_Neut_L_Ins_r1	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	1.0000000	0	0.0000000	0.0000000	0.9616787	-0.7464399	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
ALose_v_Neut_R_Ins_r1	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	1	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.000000	0.0000000	0.0000000
ALose_v_Neut_L_Ins_r2	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	1.0000000	0.6334132	0.0000000	0.0000000	0.9235014	-0.7702424	0.0000000	0.000000	0.0000000	0.0000000
ALose_v_Neut_R_Ins_r2	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.6334132	1.0000000	0.0000000	0.0000000	0.0000000	-0.6240625	0.0000000	0.000000	0.0000000	0.0000000
BLose_v_Neut_L_Ins_r1	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.9616787	0	0.0000000	0.0000000	1.0000000	-0.6929764	0.0000000	0.0000000	0.6940486	0.000000	0.0000000	0.0000000
BLose_v_Neut_R_Ins_r1	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.6712021	0.0000000	-0.7464399	0	0.0000000	0.0000000	-0.6929764	1.0000000	0.0000000	0.0000000	0.0000000	0.635043	0.0000000	0.0000000
BLose_v_Neut_L_Ins_r2	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.9235014	0.0000000	0.0000000	0.0000000	1.0000000	-0.7299038	0.0000000	0.000000	0.6955194	0.0000000
BLose_v_Neut_R_Ins_r2	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.7695138	0.0000000	0	-0.7702424	-0.6240625	0.0000000	0.0000000	-0.7299038	1.0000000	0.0000000	0.000000	-0.6111538	0.7159473
BLose_v_BWin_L_Ins_r1	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.6940486	0.0000000	0.0000000	0.0000000	1.0000000	0.000000	0.0000000	0.0000000
BLose_v_BWin_R_Ins_r1	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.6350430	0.0000000	0.0000000	0.0000000	1.000000	0.0000000	0.0000000
BLose_v_BWin_L_Ins_r2	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.6955194	-0.6111538	0.0000000	0.000000	1.0000000	0.0000000
BLose_v_BWin_R_Ins_r2	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0	0	0.0000000	0.0000000	0.0000000	0	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.7159473	0.0000000	0.000000	0.0000000	1.0000000

corrplot(as.matrix(abcd_efa_residuals), method = "shade", tl.cex = .4)

set.seed(111)
lsem_model <-"
# Factor loadings
Avoid_Insula_r2 =~ AWin_v_Neut_R_Ins_r2 + BWin_v_Neut_R_Ins_r2 + ALose_v_Neut_L_Ins_r2 + ALose_v_Neut_R_Ins_r2 + BLose_v_Neut_L_Ins_r2 + ALose_v_Neut_R_Ins_r2*BLose_v_Neut_R_Ins_r2

Appr_NAcc_r2 =~ AWin_v_Neut_L_NAc_r2 + AWin_v_Neut_R_NAc_r2 + BWin_v_Neut_L_NAc_r2 +
        AWin_v_Neut_R_NAc_r2*BWin_v_Neut_R_NAc_r2 + BWin_v_BLose_L_NAc_r2 + BWin_v_BLose_R_NAc_r2

Avoid_Insula_r1 =~ AWin_v_Neut_R_Ins_r1 + BWin_v_Neut_R_Ins_r1 + ALose_v_Neut_L_Ins_r1 + ALose_v_Neut_R_Ins_r1 
          + BLose_v_Neut_L_Ins_r1 + ALose_v_Neut_R_Ins_r1*BLose_v_Neut_R_Ins_r1

Appr_NAcc_r1 =~ AWin_v_Neut_L_NAc_r1 + AWin_v_Neut_R_NAc_r1 + AWin_v_Neut_L_NAc_r1*BWin_v_Neut_L_NAc_r1 + 
        BWin_v_Neut_R_NAc_r1 + BWin_v_BLose_L_NAc_r1 + BWin_v_BLose_R_NAc_r1


## Correlated residuals
## Nacc
AWin_v_Neut_L_NAc_r1 ~~  BWin_v_Neut_L_NAc_r1
AWin_v_Neut_L_NAc_r2 ~~  BWin_v_Neut_L_NAc_r2 
AWin_v_Neut_R_NAc_r1 ~~  BWin_v_Neut_R_NAc_r1 
AWin_v_Neut_R_NAc_r2 ~~  BWin_v_Neut_R_NAc_r2
## Insula
AWin_v_Neut_R_Ins_r1 ~~  BWin_v_Neut_R_Ins_r1
AWin_v_Neut_R_Ins_r2 ~~  BWin_v_Neut_R_Ins_r2
"

heldout_cfa <- cfa(model = lsem_model, data = abcd_df2,
                   estimator = "ML", std.lv = FALSE, meanstructure = TRUE)

model_parameters(heldout_cfa, standardize = TRUE)

## # Loading
## 
## Link                                                             | Coefficient |   SE |       95% CI |     z |      p
## ---------------------------------------------------------------------------------------------------------------------
## Avoid_Insula_r2 =~ AWin_v_Neut_R_Ins_r2                          |        0.67 | 0.03 | [0.61, 0.73] | 21.67 | < .001
## Avoid_Insula_r2 =~ BWin_v_Neut_R_Ins_r2                          |        0.57 | 0.04 | [0.50, 0.65] | 15.10 | < .001
## Avoid_Insula_r2 =~ ALose_v_Neut_L_Ins_r2                         |        0.66 | 0.03 | [0.59, 0.72] | 20.29 | < .001
## Avoid_Insula_r2 =~ ALose_v_Neut_R_Ins_r2                         |        0.94 | 0.01 | [0.92, 0.97] | 82.82 | < .001
## Avoid_Insula_r2 =~ BLose_v_Neut_L_Ins_r2                         |        0.63 | 0.03 | [0.56, 0.70] | 18.34 | < .001
## Avoid_Insula_r2 =~ BLose_v_Neut_R_Ins_r2 (ALose_v_Neut_R_Ins_r2) |        0.92 | 0.01 | [0.90, 0.95] | 74.29 | < .001
## Appr_NAcc_r2 =~ AWin_v_Neut_L_NAc_r2                             |        0.48 | 0.05 | [0.39, 0.58] |  9.88 | < .001
## Appr_NAcc_r2 =~ AWin_v_Neut_R_NAc_r2                             |        0.52 | 0.05 | [0.43, 0.62] | 11.08 | < .001
## Appr_NAcc_r2 =~ BWin_v_Neut_L_NAc_r2                             |        0.68 | 0.04 | [0.61, 0.75] | 18.27 | < .001
## Appr_NAcc_r2 =~ BWin_v_Neut_R_NAc_r2 (AWin_v_Neut_R_NAc_r2)      |        0.71 | 0.04 | [0.63, 0.78] | 19.62 | < .001
## Appr_NAcc_r2 =~ BWin_v_BLose_L_NAc_r2                            |        0.72 | 0.03 | [0.65, 0.78] | 20.67 | < .001
## Appr_NAcc_r2 =~ BWin_v_BLose_R_NAc_r2                            |        0.70 | 0.04 | [0.63, 0.77] | 19.76 | < .001
## Avoid_Insula_r1 =~ AWin_v_Neut_R_Ins_r1                          |        0.67 | 0.03 | [0.61, 0.73] | 21.36 | < .001
## Avoid_Insula_r1 =~ BWin_v_Neut_R_Ins_r1                          |        0.60 | 0.04 | [0.53, 0.67] | 16.55 | < .001
## Avoid_Insula_r1 =~ ALose_v_Neut_L_Ins_r1                         |        0.70 | 0.03 | [0.64, 0.75] | 23.57 | < .001
## Avoid_Insula_r1 =~ ALose_v_Neut_R_Ins_r1                         |        0.95 | 0.01 | [0.93, 0.97] | 87.76 | < .001
## Avoid_Insula_r1 =~ BLose_v_Neut_L_Ins_r1                         |        0.71 | 0.03 | [0.65, 0.76] | 24.63 | < .001
## Avoid_Insula_r1 =~ BLose_v_Neut_R_Ins_r1 (ALose_v_Neut_R_Ins_r1) |        0.91 | 0.01 | [0.89, 0.94] | 71.18 | < .001
## Appr_NAcc_r1 =~ AWin_v_Neut_L_NAc_r1                             |        0.57 | 0.05 | [0.47, 0.66] | 12.01 | < .001
## Appr_NAcc_r1 =~ AWin_v_Neut_R_NAc_r1                             |        0.56 | 0.05 | [0.47, 0.65] | 12.21 | < .001
## Appr_NAcc_r1 =~ BWin_v_Neut_L_NAc_r1 (AWin_v_Neut_L_NAc_r1)      |        0.74 | 0.04 | [0.67, 0.81] | 20.78 | < .001
## Appr_NAcc_r1 =~ BWin_v_Neut_R_NAc_r1                             |        0.70 | 0.04 | [0.63, 0.78] | 19.42 | < .001
## Appr_NAcc_r1 =~ BWin_v_BLose_L_NAc_r1                            |        0.70 | 0.04 | [0.63, 0.78] | 19.58 | < .001
## Appr_NAcc_r1 =~ BWin_v_BLose_R_NAc_r1                            |        0.55 | 0.04 | [0.46, 0.63] | 12.25 | < .001
## 
## # Correlation
## 
## Link                                         | Coefficient |   SE |        95% CI |     z |      p
## --------------------------------------------------------------------------------------------------
## AWin_v_Neut_L_NAc_r1 ~~ BWin_v_Neut_L_NAc_r1 |        0.90 | 0.01 | [ 0.87, 0.93] | 67.75 | < .001
## AWin_v_Neut_L_NAc_r2 ~~ BWin_v_Neut_L_NAc_r2 |        0.87 | 0.02 | [ 0.84, 0.90] | 57.23 | < .001
## AWin_v_Neut_R_NAc_r1 ~~ BWin_v_Neut_R_NAc_r1 |        0.84 | 0.02 | [ 0.81, 0.88] | 46.03 | < .001
## AWin_v_Neut_R_NAc_r2 ~~ BWin_v_Neut_R_NAc_r2 |        0.88 | 0.01 | [ 0.85, 0.91] | 59.89 | < .001
## AWin_v_Neut_R_Ins_r1 ~~ BWin_v_Neut_R_Ins_r1 |        0.79 | 0.02 | [ 0.74, 0.83] | 37.18 | < .001
## AWin_v_Neut_R_Ins_r2 ~~ BWin_v_Neut_R_Ins_r2 |        0.83 | 0.02 | [ 0.80, 0.87] | 49.36 | < .001
## Avoid_Insula_r2 ~~ Appr_NAcc_r2              |        0.05 | 0.06 | [-0.07, 0.17] |  0.76 | 0.450 
## Avoid_Insula_r2 ~~ Avoid_Insula_r1           |        0.01 | 0.06 | [-0.10, 0.12] |  0.21 | 0.831 
## Avoid_Insula_r2 ~~ Appr_NAcc_r1              |        0.04 | 0.06 | [-0.08, 0.16] |  0.67 | 0.503 
## Appr_NAcc_r2 ~~ Avoid_Insula_r1              |        0.05 | 0.06 | [-0.07, 0.17] |  0.87 | 0.385 
## Appr_NAcc_r2 ~~ Appr_NAcc_r1                 |        0.19 | 0.06 | [ 0.06, 0.31] |  2.93 | 0.003 
## Avoid_Insula_r1 ~~ Appr_NAcc_r1              |        0.04 | 0.06 | [-0.09, 0.16] |  0.57 | 0.568

cat("Chi-sq, DF, p-value, rmsea, srmr, tli and cfi statistics heldout:", 
    round(fitmeasures(heldout_cfa, fit.measures = c("chisq","df","pvalue","rmsea", "srmr", "tli", "cfi")), digits=2)
)

## Chi-sq, DF, p-value, rmsea, srmr, tli and cfi statistics heldout: 2133.01 240 0 0.15 0.1 0.73 0.77

8.2 run LSEM

8.3 Summary LSEM

Summarizing output of the lsem.estimate parents

summary(lsem.MID_par)

## -----------------------------------------------------------------
## Local Structural Equation Model 
## 
## sirt 3.12-66 (2022-05-16 12:27:54) 
## lavaan 0.6-12 (2022-07-04 16:40:02 UTC) 
## 
## R version 4.2.1 (2022-06-23) x86_64, darwin17.0 | nodename=Michaels-MacBook-Pro.local | login=root 
## 
## Function 'sirt::lsem.estimate', type='LSEM' 
## 
## 
## Call:
## sirt::lsem.estimate(data = abcd_df2, moderator = "p_puberty", 
##     moderator.grid = seq(1, 5, 1), lavmodel = lsem_model, h = 2, 
##     residualize = FALSE, sufficient_statistics = TRUE, std.lv = TRUE)
## 
## Date of Analysis: 2023-11-27 11:30:41 
## Time difference of 1.28993 secs
## Computation Time: 1.28993 
## 
## Number of observations in datasets = 330 
## Used observations in analysis = 330 
## Used sampling weights: FALSE 
## Bandwidth factor = 2 
## Bandwidth = 0.659 
## Number of focal points for moderator = 5 
## 
## Used joint estimation: FALSE 
## Used sufficient statistics: TRUE 
## Used local linear smoothing: FALSE 
## Used pseudo weights: FALSE 
## Used lavaan package: TRUE 
## Used lavaan.survey package: FALSE 
## 
## Mean structure modelled: FALSE 
## 
## lavaan Model
## 
## # Factor loadings
## Avoid_Insula_r2 =~ AWin_v_Neut_R_Ins_r2 + BWin_v_Neut_R_Ins_r2 + ALose_v_Neut_L_Ins_r2 + ALose_v_Neut_R_Ins_r2 + BLose_v_Neut_L_Ins_r2 + ALose_v_Neut_R_Ins_r2*BLose_v_Neut_R_Ins_r2
## 
## Appr_NAcc_r2 =~ AWin_v_Neut_L_NAc_r2 + AWin_v_Neut_R_NAc_r2 + BWin_v_Neut_L_NAc_r2 +
##         AWin_v_Neut_R_NAc_r2*BWin_v_Neut_R_NAc_r2 + BWin_v_BLose_L_NAc_r2 + BWin_v_BLose_R_NAc_r2
## 
## Avoid_Insula_r1 =~ AWin_v_Neut_R_Ins_r1 + BWin_v_Neut_R_Ins_r1 + ALose_v_Neut_L_Ins_r1 + ALose_v_Neut_R_Ins_r1 
##           + BLose_v_Neut_L_Ins_r1 + ALose_v_Neut_R_Ins_r1*BLose_v_Neut_R_Ins_r1
## 
## Appr_NAcc_r1 =~ AWin_v_Neut_L_NAc_r1 + AWin_v_Neut_R_NAc_r1 + AWin_v_Neut_L_NAc_r1*BWin_v_Neut_L_NAc_r1 + 
##         BWin_v_Neut_R_NAc_r1 + BWin_v_BLose_L_NAc_r1 + BWin_v_BLose_R_NAc_r1
## 
## 
## ## Correlated residuals
## ## Nacc
## AWin_v_Neut_L_NAc_r1 ~~  BWin_v_Neut_L_NAc_r1
## AWin_v_Neut_L_NAc_r2 ~~  BWin_v_Neut_L_NAc_r2 
## AWin_v_Neut_R_NAc_r1 ~~  BWin_v_Neut_R_NAc_r1 
## AWin_v_Neut_R_NAc_r2 ~~  BWin_v_Neut_R_NAc_r2
## ## Insula
## AWin_v_Neut_R_Ins_r1 ~~  BWin_v_Neut_R_Ins_r1
## AWin_v_Neut_R_Ins_r2 ~~  BWin_v_Neut_R_Ins_r2
## 
## 
## Parameter Estimate Summary
## 
##                                             par parindex      M    SD   MAD
## 1         Avoid_Insula_r2=~AWin_v_Neut_R_Ins_r2        1  0.141 0.008 0.006
## 2         Avoid_Insula_r2=~BWin_v_Neut_R_Ins_r2        2  0.142 0.015 0.013
## 3        Avoid_Insula_r2=~ALose_v_Neut_L_Ins_r2        3  0.119 0.017 0.015
## 4        Avoid_Insula_r2=~ALose_v_Neut_R_Ins_r2        4  0.179 0.018 0.015
## 5        Avoid_Insula_r2=~BLose_v_Neut_L_Ins_r2        5  0.125 0.016 0.012
## 6        Avoid_Insula_r2=~BLose_v_Neut_R_Ins_r2        6  0.194 0.013 0.011
## 7            Appr_NAcc_r2=~AWin_v_Neut_L_NAc_r2        7  0.108 0.024 0.020
## 8            Appr_NAcc_r2=~AWin_v_Neut_R_NAc_r2        8  0.115 0.020 0.017
## 9            Appr_NAcc_r2=~BWin_v_Neut_L_NAc_r2        9  0.183 0.023 0.020
## 10           Appr_NAcc_r2=~BWin_v_Neut_R_NAc_r2       10  0.182 0.023 0.021
## 11          Appr_NAcc_r2=~BWin_v_BLose_L_NAc_r2       11  0.168 0.012 0.010
## 12          Appr_NAcc_r2=~BWin_v_BLose_R_NAc_r2       12  0.165 0.035 0.030
## 13        Avoid_Insula_r1=~AWin_v_Neut_R_Ins_r1       13  0.114 0.017 0.012
## 14        Avoid_Insula_r1=~BWin_v_Neut_R_Ins_r1       14  0.121 0.016 0.016
## 15       Avoid_Insula_r1=~ALose_v_Neut_L_Ins_r1       15  0.117 0.011 0.009
## 16       Avoid_Insula_r1=~ALose_v_Neut_R_Ins_r1       16  0.165 0.006 0.006
## 17       Avoid_Insula_r1=~BLose_v_Neut_L_Ins_r1       17  0.137 0.004 0.003
## 18       Avoid_Insula_r1=~BLose_v_Neut_R_Ins_r1       18  0.187 0.014 0.013
## 19           Appr_NAcc_r1=~AWin_v_Neut_L_NAc_r1       19  0.120 0.025 0.022
## 20           Appr_NAcc_r1=~AWin_v_Neut_R_NAc_r1       20  0.109 0.022 0.021
## 21           Appr_NAcc_r1=~BWin_v_Neut_L_NAc_r1       21  0.190 0.028 0.025
## 22           Appr_NAcc_r1=~BWin_v_Neut_R_NAc_r1       22  0.166 0.020 0.017
## 23          Appr_NAcc_r1=~BWin_v_BLose_L_NAc_r1       23  0.162 0.024 0.022
## 24          Appr_NAcc_r1=~BWin_v_BLose_R_NAc_r1       24  0.139 0.037 0.033
## 25   AWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       25  0.033 0.004 0.004
## 26   AWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       26  0.029 0.005 0.004
## 27   AWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       27  0.030 0.003 0.003
## 28   AWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       28  0.033 0.005 0.004
## 29   AWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       29  0.016 0.001 0.001
## 30   AWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       30  0.023 0.002 0.002
## 31   AWin_v_Neut_R_Ins_r2~~AWin_v_Neut_R_Ins_r2       31  0.021 0.002 0.002
## 32   BWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       32  0.037 0.003 0.003
## 33 ALose_v_Neut_L_Ins_r2~~ALose_v_Neut_L_Ins_r2       33  0.017 0.002 0.001
## 34 ALose_v_Neut_R_Ins_r2~~ALose_v_Neut_R_Ins_r2       34  0.004 0.001 0.000
## 35 BLose_v_Neut_L_Ins_r2~~BLose_v_Neut_L_Ins_r2       35  0.022 0.004 0.004
## 36 BLose_v_Neut_R_Ins_r2~~BLose_v_Neut_R_Ins_r2       36  0.007 0.001 0.001
## 37   AWin_v_Neut_L_NAc_r2~~AWin_v_Neut_L_NAc_r2       37  0.035 0.004 0.003
## 38   AWin_v_Neut_R_NAc_r2~~AWin_v_Neut_R_NAc_r2       38  0.038 0.004 0.004
## 39   BWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       39  0.033 0.007 0.005
## 40   BWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       40  0.038 0.005 0.005
## 41 BWin_v_BLose_L_NAc_r2~~BWin_v_BLose_L_NAc_r2       41  0.026 0.006 0.005
## 42 BWin_v_BLose_R_NAc_r2~~BWin_v_BLose_R_NAc_r2       42  0.031 0.004 0.003
## 43   AWin_v_Neut_R_Ins_r1~~AWin_v_Neut_R_Ins_r1       43  0.016 0.001 0.001
## 44   BWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       44  0.025 0.003 0.002
## 45 ALose_v_Neut_L_Ins_r1~~ALose_v_Neut_L_Ins_r1       45  0.014 0.001 0.000
## 46 ALose_v_Neut_R_Ins_r1~~ALose_v_Neut_R_Ins_r1       46  0.003 0.001 0.000
## 47 BLose_v_Neut_L_Ins_r1~~BLose_v_Neut_L_Ins_r1       47  0.017 0.003 0.002
## 48 BLose_v_Neut_R_Ins_r1~~BLose_v_Neut_R_Ins_r1       48  0.007 0.000 0.000
## 49   AWin_v_Neut_L_NAc_r1~~AWin_v_Neut_L_NAc_r1       49  0.038 0.003 0.002
## 50   AWin_v_Neut_R_NAc_r1~~AWin_v_Neut_R_NAc_r1       50  0.035 0.002 0.002
## 51   BWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       51  0.035 0.006 0.006
## 52   BWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       52  0.036 0.004 0.003
## 53 BWin_v_BLose_L_NAc_r1~~BWin_v_BLose_L_NAc_r1       53  0.025 0.004 0.004
## 54 BWin_v_BLose_R_NAc_r1~~BWin_v_BLose_R_NAc_r1       54  0.043 0.005 0.005
## 55             Avoid_Insula_r2~~Avoid_Insula_r2       55  1.000 0.000 0.000
## 56                   Appr_NAcc_r2~~Appr_NAcc_r2       56  1.000 0.000 0.000
## 57             Avoid_Insula_r1~~Avoid_Insula_r1       57  1.000 0.000 0.000
## 58                   Appr_NAcc_r1~~Appr_NAcc_r1       58  1.000 0.000 0.000
## 59                Avoid_Insula_r2~~Appr_NAcc_r2       59  0.058 0.099 0.082
## 60             Avoid_Insula_r2~~Avoid_Insula_r1       60 -0.011 0.034 0.030
## 61                Avoid_Insula_r2~~Appr_NAcc_r1       61  0.041 0.014 0.012
## 62                Appr_NAcc_r2~~Avoid_Insula_r1       62  0.045 0.053 0.040
## 63                   Appr_NAcc_r2~~Appr_NAcc_r1       63  0.168 0.039 0.031
## 64                Avoid_Insula_r1~~Appr_NAcc_r1       64 -0.023 0.128 0.125
## 65                                        rmsea       65  0.145 0.010 0.005
## 66                                          cfi       66  0.782 0.017 0.010
## 67                                          tli       67  0.749 0.022 0.011
## 68                                          gfi       68  0.692 0.019 0.015
## 69                                         srmr       69  0.119 0.010 0.008
##       Min   Max lin_int lin_slo SD_nonlin
## 1   0.110 0.155   0.158  -0.006     0.005
## 2   0.118 0.171   0.179  -0.014     0.005
## 3   0.062 0.135   0.154  -0.013     0.010
## 4   0.129 0.199   0.218  -0.015     0.009
## 5   0.085 0.145   0.150  -0.009     0.012
## 6   0.159 0.207   0.223  -0.011     0.007
## 7   0.085 0.194   0.078   0.011     0.021
## 8   0.090 0.140   0.139  -0.009     0.017
## 9   0.161 0.259   0.158   0.010     0.021
## 10  0.158 0.220   0.222  -0.015     0.017
## 11  0.123 0.179   0.183  -0.006     0.010
## 12  0.072 0.203   0.215  -0.019     0.029
## 13  0.101 0.148   0.141  -0.010     0.013
## 14  0.105 0.146   0.125  -0.002     0.016
## 15  0.103 0.134   0.095   0.008     0.007
## 16  0.157 0.170   0.152   0.005     0.004
## 17  0.126 0.145   0.146  -0.003     0.001
## 18  0.155 0.203   0.184   0.001     0.013
## 19  0.080 0.149   0.058   0.023     0.003
## 20  0.080 0.146   0.053   0.021     0.005
## 21  0.138 0.216   0.121   0.026     0.008
## 22  0.144 0.211   0.117   0.018     0.007
## 23  0.113 0.190   0.221  -0.022     0.007
## 24  0.105 0.206   0.227  -0.033     0.011
## 25  0.030 0.040   0.042  -0.003     0.001
## 26  0.007 0.032   0.038  -0.003     0.003
## 27  0.024 0.035   0.036  -0.002     0.002
## 28  0.027 0.040   0.028   0.002     0.004
## 29  0.012 0.017   0.014   0.000     0.001
## 30  0.020 0.027   0.025  -0.001     0.002
## 31  0.018 0.026   0.023  -0.001     0.002
## 32  0.034 0.042   0.040  -0.001     0.003
## 33  0.014 0.020   0.020  -0.001     0.001
## 34  0.003 0.005   0.003   0.000     0.001
## 35  0.015 0.027   0.032  -0.004     0.002
## 36  0.006 0.007   0.007   0.000     0.001
## 37  0.017 0.039   0.043  -0.003     0.002
## 38  0.031 0.044   0.034   0.001     0.004
## 39  0.006 0.040   0.048  -0.006     0.003
## 40  0.032 0.045   0.031   0.002     0.004
## 41  0.022 0.036   0.031  -0.002     0.005
## 42  0.026 0.040   0.030   0.000     0.004
## 43  0.012 0.017   0.015   0.000     0.001
## 44  0.021 0.028   0.023   0.001     0.002
## 45  0.013 0.014   0.013   0.000     0.000
## 46  0.002 0.004   0.004   0.000     0.000
## 47  0.014 0.022   0.022  -0.002     0.002
## 48  0.006 0.007   0.006   0.000     0.000
## 49  0.036 0.044   0.044  -0.002     0.001
## 50  0.032 0.038   0.039  -0.002     0.002
## 51  0.029 0.044   0.049  -0.005     0.002
## 52  0.027 0.042   0.041  -0.002     0.003
## 53  0.018 0.028   0.015   0.004     0.002
## 54  0.028 0.048   0.049  -0.002     0.004
## 55  1.000 1.000   1.000   0.000     0.000
## 56  1.000 1.000   1.000   0.000     0.000
## 57  1.000 1.000   1.000   0.000     0.000
## 58  1.000 1.000   1.000   0.000     0.000
## 59 -0.032 0.311  -0.089   0.055     0.080
## 60 -0.060 0.028   0.071  -0.031     0.012
## 61  0.020 0.058   0.022   0.007     0.012
## 62 -0.066 0.082  -0.049   0.035     0.037
## 63  0.117 0.315   0.081   0.033     0.018
## 64 -0.191 0.096  -0.307   0.106     0.062
## 65  0.000 0.149   0.154  -0.004     0.009
## 66  0.772 1.000   0.764   0.007     0.015
## 67  0.738 1.054   0.728   0.008     0.021
## 68  0.655 0.706   0.650   0.016     0.009
## 69  0.102 0.128   0.141  -0.008     0.004
## 
## Distribution of Moderator: Density and Effective Sample Size
## 
## M=2.67 | SD=1.05
## 
##   moderator   wgt    Neff
## 1         1 0.179  84.114
## 2         2 0.231 130.525
## 3         3 0.336 161.821
## 4         4 0.251 119.136
## 5         5 0.004  28.325
## 
##    variable       M     SD    min     max
## 1 moderator   2.670  1.050  1.000   5.000
## 2       wgt   0.200  0.123  0.004   0.336
## 3      Neff 104.784 50.978 28.325 161.821

Summarizing output of the lsem.estimate youth

summary(lsem.MID_yth)

## -----------------------------------------------------------------
## Local Structural Equation Model 
## 
## sirt 3.12-66 (2022-05-16 12:27:54) 
## lavaan 0.6-12 (2022-07-04 16:40:02 UTC) 
## 
## R version 4.2.1 (2022-06-23) x86_64, darwin17.0 | nodename=Michaels-MacBook-Pro.local | login=root 
## 
## Function 'sirt::lsem.estimate', type='LSEM' 
## 
## 
## Call:
## sirt::lsem.estimate(data = abcd_df2, moderator = "y_puberty", 
##     moderator.grid = seq(1, 5, 1), lavmodel = lsem_model, h = 2, 
##     residualize = FALSE, sufficient_statistics = TRUE, std.lv = TRUE)
## 
## Date of Analysis: 2023-11-27 11:30:43 
## Time difference of 1.624377 secs
## Computation Time: 1.624377 
## 
## Number of observations in datasets = 343 
## Used observations in analysis = 343 
## Used sampling weights: FALSE 
## Bandwidth factor = 2 
## Bandwidth = 0.618 
## Number of focal points for moderator = 5 
## 
## Used joint estimation: FALSE 
## Used sufficient statistics: TRUE 
## Used local linear smoothing: FALSE 
## Used pseudo weights: FALSE 
## Used lavaan package: TRUE 
## Used lavaan.survey package: FALSE 
## 
## Mean structure modelled: FALSE 
## 
## lavaan Model
## 
## # Factor loadings
## Avoid_Insula_r2 =~ AWin_v_Neut_R_Ins_r2 + BWin_v_Neut_R_Ins_r2 + ALose_v_Neut_L_Ins_r2 + ALose_v_Neut_R_Ins_r2 + BLose_v_Neut_L_Ins_r2 + ALose_v_Neut_R_Ins_r2*BLose_v_Neut_R_Ins_r2
## 
## Appr_NAcc_r2 =~ AWin_v_Neut_L_NAc_r2 + AWin_v_Neut_R_NAc_r2 + BWin_v_Neut_L_NAc_r2 +
##         AWin_v_Neut_R_NAc_r2*BWin_v_Neut_R_NAc_r2 + BWin_v_BLose_L_NAc_r2 + BWin_v_BLose_R_NAc_r2
## 
## Avoid_Insula_r1 =~ AWin_v_Neut_R_Ins_r1 + BWin_v_Neut_R_Ins_r1 + ALose_v_Neut_L_Ins_r1 + ALose_v_Neut_R_Ins_r1 
##           + BLose_v_Neut_L_Ins_r1 + ALose_v_Neut_R_Ins_r1*BLose_v_Neut_R_Ins_r1
## 
## Appr_NAcc_r1 =~ AWin_v_Neut_L_NAc_r1 + AWin_v_Neut_R_NAc_r1 + AWin_v_Neut_L_NAc_r1*BWin_v_Neut_L_NAc_r1 + 
##         BWin_v_Neut_R_NAc_r1 + BWin_v_BLose_L_NAc_r1 + BWin_v_BLose_R_NAc_r1
## 
## 
## ## Correlated residuals
## ## Nacc
## AWin_v_Neut_L_NAc_r1 ~~  BWin_v_Neut_L_NAc_r1
## AWin_v_Neut_L_NAc_r2 ~~  BWin_v_Neut_L_NAc_r2 
## AWin_v_Neut_R_NAc_r1 ~~  BWin_v_Neut_R_NAc_r1 
## AWin_v_Neut_R_NAc_r2 ~~  BWin_v_Neut_R_NAc_r2
## ## Insula
## AWin_v_Neut_R_Ins_r1 ~~  BWin_v_Neut_R_Ins_r1
## AWin_v_Neut_R_Ins_r2 ~~  BWin_v_Neut_R_Ins_r2
## 
## 
## Parameter Estimate Summary
## 
##                                             par parindex      M    SD   MAD
## 1         Avoid_Insula_r2=~AWin_v_Neut_R_Ins_r2        1  0.133 0.016 0.013
## 2         Avoid_Insula_r2=~BWin_v_Neut_R_Ins_r2        2  0.132 0.022 0.017
## 3        Avoid_Insula_r2=~ALose_v_Neut_L_Ins_r2        3  0.111 0.023 0.020
## 4        Avoid_Insula_r2=~ALose_v_Neut_R_Ins_r2        4  0.177 0.024 0.020
## 5        Avoid_Insula_r2=~BLose_v_Neut_L_Ins_r2        5  0.119 0.015 0.011
## 6        Avoid_Insula_r2=~BLose_v_Neut_R_Ins_r2        6  0.194 0.019 0.016
## 7            Appr_NAcc_r2=~AWin_v_Neut_L_NAc_r2        7  0.107 0.024 0.019
## 8            Appr_NAcc_r2=~AWin_v_Neut_R_NAc_r2        8  0.114 0.009 0.008
## 9            Appr_NAcc_r2=~BWin_v_Neut_L_NAc_r2        9  0.181 0.021 0.017
## 10           Appr_NAcc_r2=~BWin_v_Neut_R_NAc_r2       10  0.183 0.006 0.005
## 11          Appr_NAcc_r2=~BWin_v_BLose_L_NAc_r2       11  0.170 0.014 0.010
## 12          Appr_NAcc_r2=~BWin_v_BLose_R_NAc_r2       12  0.172 0.028 0.023
## 13        Avoid_Insula_r1=~AWin_v_Neut_R_Ins_r1       13  0.113 0.003 0.003
## 14        Avoid_Insula_r1=~BWin_v_Neut_R_Ins_r1       14  0.120 0.009 0.008
## 15       Avoid_Insula_r1=~ALose_v_Neut_L_Ins_r1       15  0.116 0.009 0.007
## 16       Avoid_Insula_r1=~ALose_v_Neut_R_Ins_r1       16  0.169 0.010 0.007
## 17       Avoid_Insula_r1=~BLose_v_Neut_L_Ins_r1       17  0.136 0.009 0.007
## 18       Avoid_Insula_r1=~BLose_v_Neut_R_Ins_r1       18  0.189 0.017 0.015
## 19           Appr_NAcc_r1=~AWin_v_Neut_L_NAc_r1       19  0.125 0.018 0.017
## 20           Appr_NAcc_r1=~AWin_v_Neut_R_NAc_r1       20  0.117 0.014 0.013
## 21           Appr_NAcc_r1=~BWin_v_Neut_L_NAc_r1       21  0.193 0.021 0.020
## 22           Appr_NAcc_r1=~BWin_v_Neut_R_NAc_r1       22  0.173 0.011 0.010
## 23          Appr_NAcc_r1=~BWin_v_BLose_L_NAc_r1       23  0.169 0.018 0.014
## 24          Appr_NAcc_r1=~BWin_v_BLose_R_NAc_r1       24  0.150 0.032 0.028
## 25   AWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       25  0.034 0.005 0.005
## 26   AWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       26  0.032 0.004 0.002
## 27   AWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       27  0.031 0.003 0.002
## 28   AWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       28  0.033 0.004 0.004
## 29   AWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       29  0.016 0.002 0.002
## 30   AWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       30  0.024 0.001 0.000
## 31   AWin_v_Neut_R_Ins_r2~~AWin_v_Neut_R_Ins_r2       31  0.022 0.001 0.000
## 32   BWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       32  0.038 0.002 0.001
## 33 ALose_v_Neut_L_Ins_r2~~ALose_v_Neut_L_Ins_r2       33  0.017 0.002 0.001
## 34 ALose_v_Neut_R_Ins_r2~~ALose_v_Neut_R_Ins_r2       34  0.004 0.000 0.000
## 35 BLose_v_Neut_L_Ins_r2~~BLose_v_Neut_L_Ins_r2       35  0.022 0.003 0.002
## 36 BLose_v_Neut_R_Ins_r2~~BLose_v_Neut_R_Ins_r2       36  0.006 0.001 0.001
## 37   AWin_v_Neut_L_NAc_r2~~AWin_v_Neut_L_NAc_r2       37  0.037 0.004 0.002
## 38   AWin_v_Neut_R_NAc_r2~~AWin_v_Neut_R_NAc_r2       38  0.038 0.003 0.003
## 39   BWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       39  0.037 0.006 0.004
## 40   BWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       40  0.038 0.004 0.004
## 41 BWin_v_BLose_L_NAc_r2~~BWin_v_BLose_L_NAc_r2       41  0.026 0.004 0.003
## 42 BWin_v_BLose_R_NAc_r2~~BWin_v_BLose_R_NAc_r2       42  0.030 0.004 0.004
## 43   AWin_v_Neut_R_Ins_r1~~AWin_v_Neut_R_Ins_r1       43  0.016 0.002 0.001
## 44   BWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       44  0.026 0.002 0.002
## 45 ALose_v_Neut_L_Ins_r1~~ALose_v_Neut_L_Ins_r1       45  0.014 0.001 0.001
## 46 ALose_v_Neut_R_Ins_r1~~ALose_v_Neut_R_Ins_r1       46  0.003 0.001 0.000
## 47 BLose_v_Neut_L_Ins_r1~~BLose_v_Neut_L_Ins_r1       47  0.018 0.002 0.002
## 48 BLose_v_Neut_R_Ins_r1~~BLose_v_Neut_R_Ins_r1       48  0.007 0.001 0.001
## 49   AWin_v_Neut_L_NAc_r1~~AWin_v_Neut_L_NAc_r1       49  0.040 0.003 0.003
## 50   AWin_v_Neut_R_NAc_r1~~AWin_v_Neut_R_NAc_r1       50  0.036 0.002 0.002
## 51   BWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       51  0.036 0.007 0.007
## 52   BWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       52  0.036 0.003 0.003
## 53 BWin_v_BLose_L_NAc_r1~~BWin_v_BLose_L_NAc_r1       53  0.024 0.002 0.001
## 54 BWin_v_BLose_R_NAc_r1~~BWin_v_BLose_R_NAc_r1       54  0.041 0.008 0.005
## 55             Avoid_Insula_r2~~Avoid_Insula_r2       55  1.000 0.000 0.000
## 56                   Appr_NAcc_r2~~Appr_NAcc_r2       56  1.000 0.000 0.000
## 57             Avoid_Insula_r1~~Avoid_Insula_r1       57  1.000 0.000 0.000
## 58                   Appr_NAcc_r1~~Appr_NAcc_r1       58  1.000 0.000 0.000
## 59                Avoid_Insula_r2~~Appr_NAcc_r2       59  0.032 0.100 0.089
## 60             Avoid_Insula_r2~~Avoid_Insula_r1       60  0.006 0.051 0.049
## 61                Avoid_Insula_r2~~Appr_NAcc_r1       61  0.025 0.079 0.066
## 62                Appr_NAcc_r2~~Avoid_Insula_r1       62  0.058 0.057 0.051
## 63                   Appr_NAcc_r2~~Appr_NAcc_r1       63  0.164 0.042 0.033
## 64                Avoid_Insula_r1~~Appr_NAcc_r1       64 -0.009 0.071 0.060
## 65                                        rmsea       65  0.145 0.014 0.007
## 66                                          cfi       66  0.781 0.028 0.015
## 67                                          tli       67  0.748 0.032 0.017
## 68                                          gfi       68  0.690 0.027 0.019
## 69                                         srmr       69  0.120 0.010 0.007
##       Min   Max lin_int lin_slo SD_nonlin
## 1   0.116 0.169   0.174  -0.015     0.005
## 2   0.109 0.184   0.189  -0.021     0.008
## 3   0.060 0.158   0.174  -0.023     0.005
## 4   0.127 0.209   0.243  -0.024     0.005
## 5   0.069 0.146   0.159  -0.015     0.003
## 6   0.148 0.212   0.241  -0.017     0.010
## 7   0.087 0.193   0.049   0.021     0.012
## 8   0.108 0.151   0.106   0.003     0.009
## 9   0.163 0.252   0.132   0.018     0.011
## 10  0.168 0.189   0.180   0.001     0.006
## 11  0.107 0.181   0.200  -0.011     0.009
## 12  0.064 0.190   0.216  -0.016     0.023
## 13  0.101 0.117   0.113   0.000     0.003
## 14  0.104 0.131   0.096   0.009     0.002
## 15  0.107 0.131   0.095   0.008     0.005
## 16  0.144 0.175   0.156   0.005     0.009
## 17  0.115 0.156   0.159  -0.008     0.004
## 18  0.150 0.202   0.197  -0.003     0.017
## 19  0.089 0.142   0.087   0.014     0.012
## 20  0.094 0.133   0.094   0.008     0.012
## 21  0.153 0.212   0.148   0.017     0.014
## 22  0.159 0.183   0.152   0.008     0.007
## 23  0.108 0.186   0.210  -0.015     0.010
## 24  0.081 0.194   0.237  -0.032     0.006
## 25  0.029 0.041   0.046  -0.004     0.003
## 26  0.007 0.035   0.036  -0.002     0.004
## 27  0.029 0.034   0.035  -0.002     0.002
## 28  0.027 0.038   0.032   0.000     0.004
## 29  0.012 0.018   0.016   0.000     0.002
## 30  0.022 0.025   0.026  -0.001     0.000
## 31  0.021 0.023   0.023   0.000     0.000
## 32  0.031 0.040   0.039   0.000     0.002
## 33  0.013 0.020   0.021  -0.001     0.001
## 34  0.003 0.004   0.004   0.000     0.000
## 35  0.015 0.026   0.029  -0.002     0.002
## 36  0.005 0.007   0.006   0.000     0.001
## 37  0.016 0.039   0.039  -0.001     0.004
## 38  0.032 0.042   0.038   0.000     0.003
## 39  0.006 0.040   0.047  -0.004     0.004
## 40  0.032 0.043   0.037   0.000     0.004
## 41  0.020 0.031   0.034  -0.003     0.003
## 42  0.026 0.041   0.027   0.001     0.004
## 43  0.013 0.018   0.016   0.000     0.002
## 44  0.020 0.030   0.029  -0.001     0.002
## 45  0.012 0.015   0.014   0.000     0.001
## 46  0.002 0.004   0.005  -0.001     0.000
## 47  0.015 0.021   0.024  -0.002     0.001
## 48  0.005 0.008   0.007   0.000     0.001
## 49  0.037 0.043   0.046  -0.002     0.002
## 50  0.034 0.039   0.037   0.000     0.002
## 51  0.028 0.046   0.053  -0.006     0.004
## 52  0.031 0.041   0.042  -0.002     0.002
## 53  0.022 0.026   0.024   0.000     0.002
## 54  0.025 0.061   0.061  -0.007     0.003
## 55  1.000 1.000   1.000   0.000     0.000
## 56  1.000 1.000   1.000   0.000     0.000
## 57  1.000 1.000   1.000   0.000     0.000
## 58  1.000 1.000   1.000   0.000     0.000
## 59 -0.065 0.328  -0.038   0.025     0.097
## 60 -0.046 0.073   0.000   0.002     0.051
## 61 -0.074 0.210   0.226  -0.073     0.031
## 62  0.001 0.144   0.167  -0.040     0.042
## 63  0.105 0.222   0.099   0.024     0.035
## 64 -0.116 0.140  -0.149   0.051     0.050
## 65  0.059 0.150   0.165  -0.008     0.012
## 66  0.770 0.949   0.737   0.016     0.023
## 67  0.736 0.941   0.698   0.018     0.027
## 68  0.620 0.703   0.657   0.012     0.025
## 69  0.113 0.146   0.140  -0.008     0.007
## 
## Distribution of Moderator: Density and Effective Sample Size
## 
## M=2.755 | SD=0.993
## 
##   moderator   wgt    Neff
## 1         1 0.114  65.606
## 2         2 0.280 140.968
## 3         3 0.367 172.175
## 4         4 0.216 110.711
## 5         5 0.023  28.663
## 
##    variable       M     SD    min     max
## 1 moderator   2.755  0.993  1.000   5.000
## 2       wgt   0.200  0.135  0.023   0.367
## 3      Neff 103.624 57.464 28.663 172.175

8.4 Permutation Test LSEM

Running permutation test of LSEM model. N = 1000 bootstraps

8.4.1 parent

plot(lsem.permuted_par,type = "global",title = "Global Statistics for Parent PDS")

summary(lsem.permuted_par)# examine results

## -----------------------------------------------------------------
## Permutation Test for Local Structural Equation Model 
## 
## sirt 3.12-66 (2022-05-16 12:27:54) 
## lavaan 0.6-12 (2022-07-04 16:40:02 UTC) 
## 
## Function 'sirt::lsem.permutationTest' 
## 
## 
## Call:
## sirt::lsem.permutationTest(lsem.object = lsem.MID_par, B = n_permutations, 
##     residualize = FALSE)
## 
## Date of Analysis: 2023-11-27 12:22:54 
## Time difference of 52.18156 mins
## Computation Time: 52.18156 
## 
## Number of permutations = 1000 
## Percentage of non-converged datasets = 9.256 
## Number of observations=330 
## Bandwidth factor=2 
## Bandwidth=0.659 
## Number of focal points for moderator=5 
## 
## lavaan Model
## 
## # Factor loadings
## Avoid_Insula_r2 =~ AWin_v_Neut_R_Ins_r2 + BWin_v_Neut_R_Ins_r2 + ALose_v_Neut_L_Ins_r2 + ALose_v_Neut_R_Ins_r2 + BLose_v_Neut_L_Ins_r2 + ALose_v_Neut_R_Ins_r2*BLose_v_Neut_R_Ins_r2
## 
## Appr_NAcc_r2 =~ AWin_v_Neut_L_NAc_r2 + AWin_v_Neut_R_NAc_r2 + BWin_v_Neut_L_NAc_r2 +
##         AWin_v_Neut_R_NAc_r2*BWin_v_Neut_R_NAc_r2 + BWin_v_BLose_L_NAc_r2 + BWin_v_BLose_R_NAc_r2
## 
## Avoid_Insula_r1 =~ AWin_v_Neut_R_Ins_r1 + BWin_v_Neut_R_Ins_r1 + ALose_v_Neut_L_Ins_r1 + ALose_v_Neut_R_Ins_r1 
##           + BLose_v_Neut_L_Ins_r1 + ALose_v_Neut_R_Ins_r1*BLose_v_Neut_R_Ins_r1
## 
## Appr_NAcc_r1 =~ AWin_v_Neut_L_NAc_r1 + AWin_v_Neut_R_NAc_r1 + AWin_v_Neut_L_NAc_r1*BWin_v_Neut_L_NAc_r1 + 
##         BWin_v_Neut_R_NAc_r1 + BWin_v_BLose_L_NAc_r1 + BWin_v_BLose_R_NAc_r1
## 
## 
## ## Correlated residuals
## ## Nacc
## AWin_v_Neut_L_NAc_r1 ~~  BWin_v_Neut_L_NAc_r1
## AWin_v_Neut_L_NAc_r2 ~~  BWin_v_Neut_L_NAc_r2 
## AWin_v_Neut_R_NAc_r1 ~~  BWin_v_Neut_R_NAc_r1 
## AWin_v_Neut_R_NAc_r2 ~~  BWin_v_Neut_R_NAc_r2
## ## Insula
## AWin_v_Neut_R_Ins_r1 ~~  BWin_v_Neut_R_Ins_r1
## AWin_v_Neut_R_Ins_r2 ~~  BWin_v_Neut_R_Ins_r2
## 
## 
## Global Test Statistics
## 
##                                             par      M    SD  SD_p   MAD MAD_p
## 1         Avoid_Insula_r2=~AWin_v_Neut_R_Ins_r2  0.141 0.008 0.699 0.006 0.741
## 2         Avoid_Insula_r2=~BWin_v_Neut_R_Ins_r2  0.142 0.015 0.373 0.013 0.365
## 3        Avoid_Insula_r2=~ALose_v_Neut_L_Ins_r2  0.119 0.017 0.157 0.015 0.157
## 4        Avoid_Insula_r2=~ALose_v_Neut_R_Ins_r2  0.179 0.018 0.102 0.015 0.116
## 5        Avoid_Insula_r2=~BLose_v_Neut_L_Ins_r2  0.125 0.016 0.220 0.012 0.269
## 6        Avoid_Insula_r2=~BLose_v_Neut_R_Ins_r2  0.194 0.013 0.249 0.011 0.244
## 7            Appr_NAcc_r2=~AWin_v_Neut_L_NAc_r2  0.108 0.024 0.246 0.020 0.278
## 8            Appr_NAcc_r2=~AWin_v_Neut_R_NAc_r2  0.115 0.020 0.487 0.017 0.477
## 9            Appr_NAcc_r2=~BWin_v_Neut_L_NAc_r2  0.183 0.023 0.209 0.020 0.215
## 10           Appr_NAcc_r2=~BWin_v_Neut_R_NAc_r2  0.182 0.023 0.320 0.021 0.269
## 11          Appr_NAcc_r2=~BWin_v_BLose_L_NAc_r2  0.168 0.012 0.620 0.010 0.649
## 12          Appr_NAcc_r2=~BWin_v_BLose_R_NAc_r2  0.165 0.035 0.040 0.030 0.041
## 13        Avoid_Insula_r1=~AWin_v_Neut_R_Ins_r1  0.114 0.017 0.080 0.012 0.148
## 14        Avoid_Insula_r1=~BWin_v_Neut_R_Ins_r1  0.121 0.016 0.227 0.016 0.157
## 15       Avoid_Insula_r1=~ALose_v_Neut_L_Ins_r1  0.117 0.011 0.324 0.009 0.389
## 16       Avoid_Insula_r1=~ALose_v_Neut_R_Ins_r1  0.165 0.006 0.656 0.006 0.549
## 17       Avoid_Insula_r1=~BLose_v_Neut_L_Ins_r1  0.137 0.004 0.947 0.003 0.952
## 18       Avoid_Insula_r1=~BLose_v_Neut_R_Ins_r1  0.187 0.014 0.218 0.013 0.161
## 19           Appr_NAcc_r1=~AWin_v_Neut_L_NAc_r1  0.120 0.025 0.409 0.022 0.364
## 20           Appr_NAcc_r1=~AWin_v_Neut_R_NAc_r1  0.109 0.022 0.345 0.021 0.279
## 21           Appr_NAcc_r1=~BWin_v_Neut_L_NAc_r1  0.190 0.028 0.313 0.025 0.267
## 22           Appr_NAcc_r1=~BWin_v_Neut_R_NAc_r1  0.166 0.020 0.433 0.017 0.457
## 23          Appr_NAcc_r1=~BWin_v_BLose_L_NAc_r1  0.162 0.024 0.268 0.022 0.231
## 24          Appr_NAcc_r1=~BWin_v_BLose_R_NAc_r1  0.139 0.037 0.136 0.033 0.118
## 25   AWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1  0.033 0.004 0.802 0.004 0.765
## 26   AWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2  0.029 0.005 0.443 0.004 0.442
## 27   AWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1  0.030 0.003 0.746 0.003 0.682
## 28   AWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2  0.033 0.005 0.477 0.004 0.418
## 29   AWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1  0.016 0.001 0.579 0.001 0.575
## 30   AWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2  0.023 0.002 0.570 0.002 0.536
## 31   AWin_v_Neut_R_Ins_r2~~AWin_v_Neut_R_Ins_r2  0.021 0.002 0.559 0.002 0.490
## 32   BWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2  0.037 0.003 0.609 0.003 0.599
## 33 ALose_v_Neut_L_Ins_r2~~ALose_v_Neut_L_Ins_r2  0.017 0.002 0.413 0.001 0.428
## 34 ALose_v_Neut_R_Ins_r2~~ALose_v_Neut_R_Ins_r2  0.004 0.001 0.540 0.000 0.711
## 35 BLose_v_Neut_L_Ins_r2~~BLose_v_Neut_L_Ins_r2  0.022 0.004 0.070 0.004 0.057
## 36 BLose_v_Neut_R_Ins_r2~~BLose_v_Neut_R_Ins_r2  0.007 0.001 0.840 0.001 0.806
## 37   AWin_v_Neut_L_NAc_r2~~AWin_v_Neut_L_NAc_r2  0.035 0.004 0.604 0.003 0.606
## 38   AWin_v_Neut_R_NAc_r2~~AWin_v_Neut_R_NAc_r2  0.038 0.004 0.499 0.004 0.476
## 39   BWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2  0.033 0.007 0.198 0.005 0.218
## 40   BWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2  0.038 0.005 0.528 0.005 0.479
## 41 BWin_v_BLose_L_NAc_r2~~BWin_v_BLose_L_NAc_r2  0.026 0.006 0.229 0.005 0.237
## 42 BWin_v_BLose_R_NAc_r2~~BWin_v_BLose_R_NAc_r2  0.031 0.004 0.404 0.003 0.379
## 43   AWin_v_Neut_R_Ins_r1~~AWin_v_Neut_R_Ins_r1  0.016 0.001 0.531 0.001 0.444
## 44   BWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1  0.025 0.003 0.472 0.002 0.477
## 45 ALose_v_Neut_L_Ins_r1~~ALose_v_Neut_L_Ins_r1  0.014 0.001 0.960 0.000 0.954
## 46 ALose_v_Neut_R_Ins_r1~~ALose_v_Neut_R_Ins_r1  0.003 0.001 0.539 0.000 0.561
## 47 BLose_v_Neut_L_Ins_r1~~BLose_v_Neut_L_Ins_r1  0.017 0.003 0.262 0.002 0.325
## 48 BLose_v_Neut_R_Ins_r1~~BLose_v_Neut_R_Ins_r1  0.007 0.000 0.964 0.000 0.971
## 49   AWin_v_Neut_L_NAc_r1~~AWin_v_Neut_L_NAc_r1  0.038 0.003 0.873 0.002 0.905
## 50   AWin_v_Neut_R_NAc_r1~~AWin_v_Neut_R_NAc_r1  0.035 0.002 0.850 0.002 0.826
## 51   BWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1  0.035 0.006 0.669 0.006 0.567
## 52   BWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1  0.036 0.004 0.719 0.003 0.746
## 53 BWin_v_BLose_L_NAc_r1~~BWin_v_BLose_L_NAc_r1  0.025 0.004 0.602 0.004 0.524
## 54 BWin_v_BLose_R_NAc_r1~~BWin_v_BLose_R_NAc_r1  0.043 0.005 0.736 0.005 0.660
## 55             Avoid_Insula_r2~~Avoid_Insula_r2  1.000 0.000 1.000 0.000 1.000
## 56                   Appr_NAcc_r2~~Appr_NAcc_r2  1.000 0.000 1.000 0.000 1.000
## 57             Avoid_Insula_r1~~Avoid_Insula_r1  1.000 0.000 1.000 0.000 1.000
## 58                   Appr_NAcc_r1~~Appr_NAcc_r1  1.000 0.000 1.000 0.000 1.000
## 59                Avoid_Insula_r2~~Appr_NAcc_r2  0.058 0.099 0.284 0.082 0.290
## 60             Avoid_Insula_r2~~Avoid_Insula_r1 -0.011 0.034 0.817 0.030 0.801
## 61                Avoid_Insula_r2~~Appr_NAcc_r1  0.041 0.014 0.988 0.012 0.984
## 62                Appr_NAcc_r2~~Avoid_Insula_r1  0.045 0.053 0.673 0.040 0.736
## 63                   Appr_NAcc_r2~~Appr_NAcc_r1  0.168 0.039 0.893 0.031 0.904
## 64                Avoid_Insula_r1~~Appr_NAcc_r1 -0.023 0.128 0.213 0.125 0.126
## 65                                        rmsea  0.145 0.010 0.070 0.005 0.727
## 66                                          cfi  0.782 0.017 0.407 0.010 0.778
## 67                                          tli  0.749 0.022 0.273 0.011 0.764
## 68                                          gfi  0.692 0.019 0.460 0.015 0.483
## 69                                         srmr  0.119 0.010 0.444 0.008 0.452
##    lin_slo lin_slo_p
## 1   -0.006     0.504
## 2   -0.014     0.238
## 3   -0.013     0.190
## 4   -0.015     0.114
## 5   -0.009     0.296
## 6   -0.011     0.200
## 7    0.011     0.468
## 8   -0.009     0.614
## 9    0.010     0.478
## 10  -0.015     0.352
## 11  -0.006     0.630
## 12  -0.019     0.180
## 13  -0.010     0.174
## 14  -0.002     0.822
## 15   0.008     0.308
## 16   0.005     0.486
## 17  -0.003     0.702
## 18   0.001     0.872
## 19   0.023     0.200
## 20   0.021     0.196
## 21   0.026     0.150
## 22   0.018     0.274
## 23  -0.022     0.170
## 24  -0.033     0.068
## 25  -0.003     0.490
## 26  -0.003     0.362
## 27  -0.002     0.548
## 28   0.002     0.686
## 29   0.000     0.792
## 30  -0.001     0.686
## 31  -0.001     0.686
## 32  -0.001     0.682
## 33  -0.001     0.474
## 34   0.000     0.868
## 35  -0.004     0.058
## 36   0.000     0.992
## 37  -0.003     0.388
## 38   0.001     0.736
## 39  -0.006     0.130
## 40   0.002     0.602
## 41  -0.002     0.578
## 42   0.000     0.852
## 43   0.000     0.914
## 44   0.001     0.720
## 45   0.000     0.912
## 46   0.000     0.548
## 47  -0.002     0.232
## 48   0.000     0.848
## 49  -0.002     0.568
## 50  -0.002     0.644
## 51  -0.005     0.380
## 52  -0.002     0.630
## 53   0.004     0.378
## 54  -0.002     0.704
## 55   0.000     1.000
## 56   0.000     1.000
## 57   0.000     1.000
## 58   0.000     1.000
## 59   0.055     0.414
## 60  -0.031     0.586
## 61   0.007     0.892
## 62   0.035     0.534
## 63   0.033     0.612
## 64   0.106     0.168
## 65  -0.004     0.730
## 66   0.007     0.918
## 67   0.008     0.886
## 68   0.016     0.254
## 69  -0.008     0.342
## 
## Pointwise Test Statistics
## 
##                                              par parindex moderator    est
## 1          Avoid_Insula_r2=~AWin_v_Neut_R_Ins_r2        1         1  0.014
## 2          Avoid_Insula_r2=~AWin_v_Neut_R_Ins_r2        1         2 -0.003
## 3          Avoid_Insula_r2=~AWin_v_Neut_R_Ins_r2        1         3  0.002
## 4          Avoid_Insula_r2=~AWin_v_Neut_R_Ins_r2        1         4 -0.010
## 5          Avoid_Insula_r2=~AWin_v_Neut_R_Ins_r2        1         5 -0.030
## 6          Avoid_Insula_r2=~BWin_v_Neut_R_Ins_r2        2         1  0.029
## 7          Avoid_Insula_r2=~BWin_v_Neut_R_Ins_r2        2         2  0.006
## 8          Avoid_Insula_r2=~BWin_v_Neut_R_Ins_r2        2         3 -0.009
## 9          Avoid_Insula_r2=~BWin_v_Neut_R_Ins_r2        2         4 -0.014
## 10         Avoid_Insula_r2=~BWin_v_Neut_R_Ins_r2        2         5 -0.024
## 11        Avoid_Insula_r2=~ALose_v_Neut_L_Ins_r2        3         1  0.009
## 12        Avoid_Insula_r2=~ALose_v_Neut_L_Ins_r2        3         2  0.016
## 13        Avoid_Insula_r2=~ALose_v_Neut_L_Ins_r2        3         3  0.006
## 14        Avoid_Insula_r2=~ALose_v_Neut_L_Ins_r2        3         4 -0.028
## 15        Avoid_Insula_r2=~ALose_v_Neut_L_Ins_r2        3         5 -0.057
## 16        Avoid_Insula_r2=~ALose_v_Neut_R_Ins_r2        4         1  0.020
## 17        Avoid_Insula_r2=~ALose_v_Neut_R_Ins_r2        4         2  0.006
## 18        Avoid_Insula_r2=~ALose_v_Neut_R_Ins_r2        4         3  0.007
## 19        Avoid_Insula_r2=~ALose_v_Neut_R_Ins_r2        4         4 -0.029
## 20        Avoid_Insula_r2=~ALose_v_Neut_R_Ins_r2        4         5 -0.050
## 21        Avoid_Insula_r2=~BLose_v_Neut_L_Ins_r2        5         1 -0.001
## 22        Avoid_Insula_r2=~BLose_v_Neut_L_Ins_r2        5         2  0.020
## 23        Avoid_Insula_r2=~BLose_v_Neut_L_Ins_r2        5         3  0.005
## 24        Avoid_Insula_r2=~BLose_v_Neut_L_Ins_r2        5         4 -0.023
## 25        Avoid_Insula_r2=~BLose_v_Neut_L_Ins_r2        5         5 -0.040
## 26        Avoid_Insula_r2=~BLose_v_Neut_R_Ins_r2        6         1  0.013
## 27        Avoid_Insula_r2=~BLose_v_Neut_R_Ins_r2        6         2  0.007
## 28        Avoid_Insula_r2=~BLose_v_Neut_R_Ins_r2        6         3  0.005
## 29        Avoid_Insula_r2=~BLose_v_Neut_R_Ins_r2        6         4 -0.022
## 30        Avoid_Insula_r2=~BLose_v_Neut_R_Ins_r2        6         5 -0.035
## 31            Appr_NAcc_r2=~AWin_v_Neut_L_NAc_r2        7         1  0.000
## 32            Appr_NAcc_r2=~AWin_v_Neut_L_NAc_r2        7         2 -0.009
## 33            Appr_NAcc_r2=~AWin_v_Neut_L_NAc_r2        7         3 -0.023
## 34            Appr_NAcc_r2=~AWin_v_Neut_L_NAc_r2        7         4  0.038
## 35            Appr_NAcc_r2=~AWin_v_Neut_L_NAc_r2        7         5  0.086
## 36            Appr_NAcc_r2=~AWin_v_Neut_R_NAc_r2        8         1  0.012
## 37            Appr_NAcc_r2=~AWin_v_Neut_R_NAc_r2        8         2  0.025
## 38            Appr_NAcc_r2=~AWin_v_Neut_R_NAc_r2        8         3 -0.025
## 39            Appr_NAcc_r2=~AWin_v_Neut_R_NAc_r2        8         4  0.002
## 40            Appr_NAcc_r2=~AWin_v_Neut_R_NAc_r2        8         5  0.017
## 41            Appr_NAcc_r2=~BWin_v_Neut_L_NAc_r2        9         1  0.003
## 42            Appr_NAcc_r2=~BWin_v_Neut_L_NAc_r2        9         2 -0.009
## 43            Appr_NAcc_r2=~BWin_v_Neut_L_NAc_r2        9         3 -0.023
## 44            Appr_NAcc_r2=~BWin_v_Neut_L_NAc_r2        9         4  0.036
## 45            Appr_NAcc_r2=~BWin_v_Neut_L_NAc_r2        9         5  0.075
## 46            Appr_NAcc_r2=~BWin_v_Neut_R_NAc_r2       10         1  0.010
## 47            Appr_NAcc_r2=~BWin_v_Neut_R_NAc_r2       10         2  0.038
## 48            Appr_NAcc_r2=~BWin_v_Neut_R_NAc_r2       10         3 -0.019
## 49            Appr_NAcc_r2=~BWin_v_Neut_R_NAc_r2       10         4 -0.017
## 50            Appr_NAcc_r2=~BWin_v_Neut_R_NAc_r2       10         5 -0.024
## 51           Appr_NAcc_r2=~BWin_v_BLose_L_NAc_r2       11         1  0.001
## 52           Appr_NAcc_r2=~BWin_v_BLose_L_NAc_r2       11         2  0.004
## 53           Appr_NAcc_r2=~BWin_v_BLose_L_NAc_r2       11         3  0.011
## 54           Appr_NAcc_r2=~BWin_v_BLose_L_NAc_r2       11         4 -0.019
## 55           Appr_NAcc_r2=~BWin_v_BLose_L_NAc_r2       11         5 -0.045
## 56           Appr_NAcc_r2=~BWin_v_BLose_R_NAc_r2       12         1 -0.006
## 57           Appr_NAcc_r2=~BWin_v_BLose_R_NAc_r2       12         2  0.038
## 58           Appr_NAcc_r2=~BWin_v_BLose_R_NAc_r2       12         3  0.018
## 59           Appr_NAcc_r2=~BWin_v_BLose_R_NAc_r2       12         4 -0.054
## 60           Appr_NAcc_r2=~BWin_v_BLose_R_NAc_r2       12         5 -0.093
## 61         Avoid_Insula_r1=~AWin_v_Neut_R_Ins_r1       13         1  0.034
## 62         Avoid_Insula_r1=~AWin_v_Neut_R_Ins_r1       13         2 -0.006
## 63         Avoid_Insula_r1=~AWin_v_Neut_R_Ins_r1       13         3 -0.013
## 64         Avoid_Insula_r1=~AWin_v_Neut_R_Ins_r1       13         4 -0.001
## 65         Avoid_Insula_r1=~AWin_v_Neut_R_Ins_r1       13         5  0.001
## 66         Avoid_Insula_r1=~BWin_v_Neut_R_Ins_r1       14         1  0.025
## 67         Avoid_Insula_r1=~BWin_v_Neut_R_Ins_r1       14         2 -0.017
## 68         Avoid_Insula_r1=~BWin_v_Neut_R_Ins_r1       14         3 -0.012
## 69         Avoid_Insula_r1=~BWin_v_Neut_R_Ins_r1       14         4  0.013
## 70         Avoid_Insula_r1=~BWin_v_Neut_R_Ins_r1       14         5  0.023
## 71        Avoid_Insula_r1=~ALose_v_Neut_L_Ins_r1       15         1 -0.004
## 72        Avoid_Insula_r1=~ALose_v_Neut_L_Ins_r1       15         2 -0.014
## 73        Avoid_Insula_r1=~ALose_v_Neut_L_Ins_r1       15         3 -0.001
## 74        Avoid_Insula_r1=~ALose_v_Neut_L_Ins_r1       15         4  0.017
## 75        Avoid_Insula_r1=~ALose_v_Neut_L_Ins_r1       15         5  0.015
## 76        Avoid_Insula_r1=~ALose_v_Neut_R_Ins_r1       16         1 -0.006
## 77        Avoid_Insula_r1=~ALose_v_Neut_R_Ins_r1       16         2 -0.008
## 78        Avoid_Insula_r1=~ALose_v_Neut_R_Ins_r1       16         3  0.005
## 79        Avoid_Insula_r1=~ALose_v_Neut_R_Ins_r1       16         4  0.005
## 80        Avoid_Insula_r1=~ALose_v_Neut_R_Ins_r1       16         5 -0.002
## 81        Avoid_Insula_r1=~BLose_v_Neut_L_Ins_r1       17         1  0.008
## 82        Avoid_Insula_r1=~BLose_v_Neut_L_Ins_r1       17         2  0.001
## 83        Avoid_Insula_r1=~BLose_v_Neut_L_Ins_r1       17         3 -0.002
## 84        Avoid_Insula_r1=~BLose_v_Neut_L_Ins_r1       17         4 -0.003
## 85        Avoid_Insula_r1=~BLose_v_Neut_L_Ins_r1       17         5 -0.012
## 86        Avoid_Insula_r1=~BLose_v_Neut_R_Ins_r1       18         1 -0.016
## 87        Avoid_Insula_r1=~BLose_v_Neut_R_Ins_r1       18         2  0.004
## 88        Avoid_Insula_r1=~BLose_v_Neut_R_Ins_r1       18         3  0.016
## 89        Avoid_Insula_r1=~BLose_v_Neut_R_Ins_r1       18         4 -0.013
## 90        Avoid_Insula_r1=~BLose_v_Neut_R_Ins_r1       18         5 -0.032
## 91            Appr_NAcc_r1=~AWin_v_Neut_L_NAc_r1       19         1 -0.040
## 92            Appr_NAcc_r1=~AWin_v_Neut_L_NAc_r1       19         2 -0.016
## 93            Appr_NAcc_r1=~AWin_v_Neut_L_NAc_r1       19         3  0.011
## 94            Appr_NAcc_r1=~AWin_v_Neut_L_NAc_r1       19         4  0.029
## 95            Appr_NAcc_r1=~AWin_v_Neut_L_NAc_r1       19         5  0.027
## 96            Appr_NAcc_r1=~AWin_v_Neut_R_NAc_r1       20         1 -0.028
## 97            Appr_NAcc_r1=~AWin_v_Neut_R_NAc_r1       20         2 -0.023
## 98            Appr_NAcc_r1=~AWin_v_Neut_R_NAc_r1       20         3  0.009
## 99            Appr_NAcc_r1=~AWin_v_Neut_R_NAc_r1       20         4  0.029
## 100           Appr_NAcc_r1=~AWin_v_Neut_R_NAc_r1       20         5  0.038
## 101           Appr_NAcc_r1=~BWin_v_Neut_L_NAc_r1       21         1 -0.052
## 102           Appr_NAcc_r1=~BWin_v_Neut_L_NAc_r1       21         2 -0.014
## 103           Appr_NAcc_r1=~BWin_v_Neut_L_NAc_r1       21         3  0.017
## 104           Appr_NAcc_r1=~BWin_v_Neut_L_NAc_r1       21         4  0.027
## 105           Appr_NAcc_r1=~BWin_v_Neut_L_NAc_r1       21         5  0.018
## 106           Appr_NAcc_r1=~BWin_v_Neut_R_NAc_r1       22         1 -0.021
## 107           Appr_NAcc_r1=~BWin_v_Neut_R_NAc_r1       22         2 -0.020
## 108           Appr_NAcc_r1=~BWin_v_Neut_R_NAc_r1       22         3  0.002
## 109           Appr_NAcc_r1=~BWin_v_Neut_R_NAc_r1       22         4  0.031
## 110           Appr_NAcc_r1=~BWin_v_Neut_R_NAc_r1       22         5  0.046
## 111          Appr_NAcc_r1=~BWin_v_BLose_L_NAc_r1       23         1  0.028
## 112          Appr_NAcc_r1=~BWin_v_BLose_L_NAc_r1       23         2  0.026
## 113          Appr_NAcc_r1=~BWin_v_BLose_L_NAc_r1       23         3 -0.008
## 114          Appr_NAcc_r1=~BWin_v_BLose_L_NAc_r1       23         4 -0.032
## 115          Appr_NAcc_r1=~BWin_v_BLose_L_NAc_r1       23         5 -0.049
## 116          Appr_NAcc_r1=~BWin_v_BLose_R_NAc_r1       24         1  0.067
## 117          Appr_NAcc_r1=~BWin_v_BLose_R_NAc_r1       24         2  0.019
## 118          Appr_NAcc_r1=~BWin_v_BLose_R_NAc_r1       24         3 -0.024
## 119          Appr_NAcc_r1=~BWin_v_BLose_R_NAc_r1       24         4 -0.032
## 120          Appr_NAcc_r1=~BWin_v_BLose_R_NAc_r1       24         5 -0.034
## 121   AWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       25         1  0.006
## 122   AWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       25         2  0.003
## 123   AWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       25         3 -0.003
## 124   AWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       25         4 -0.003
## 125   AWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       25         5 -0.004
## 126   AWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       26         1  0.003
## 127   AWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       26         2  0.003
## 128   AWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       26         3  0.002
## 129   AWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       26         4 -0.007
## 130   AWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       26         5 -0.022
## 131   AWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       27         1  0.002
## 132   AWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       27         2  0.004
## 133   AWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       27         3 -0.002
## 134   AWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       27         4 -0.003
## 135   AWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       27         5 -0.006
## 136   AWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       28         1 -0.006
## 137   AWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       28         2 -0.002
## 138   AWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       28         3  0.006
## 139   AWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       28         4 -0.002
## 140   AWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       28         5 -0.006
## 141   AWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       29         1 -0.002
## 142   AWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       29         2  0.000
## 143   AWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       29         3  0.002
## 144   AWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       29         4 -0.001
## 145   AWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       29         5 -0.003
## 146   AWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       30         1  0.001
## 147   AWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       30         2  0.003
## 148   AWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       30         3 -0.003
## 149   AWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       30         4  0.001
## 150   AWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       30         5  0.004
## 151   AWin_v_Neut_R_Ins_r2~~AWin_v_Neut_R_Ins_r2       31         1  0.001
## 152   AWin_v_Neut_R_Ins_r2~~AWin_v_Neut_R_Ins_r2       31         2  0.002
## 153   AWin_v_Neut_R_Ins_r2~~AWin_v_Neut_R_Ins_r2       31         3 -0.003
## 154   AWin_v_Neut_R_Ins_r2~~AWin_v_Neut_R_Ins_r2       31         4  0.001
## 155   AWin_v_Neut_R_Ins_r2~~AWin_v_Neut_R_Ins_r2       31         5  0.005
## 156   BWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       32         1  0.001
## 157   BWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       32         2  0.004
## 158   BWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       32         3 -0.004
## 159   BWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       32         4  0.001
## 160   BWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       32         5  0.003
## 161 ALose_v_Neut_L_Ins_r2~~ALose_v_Neut_L_Ins_r2       33         1  0.000
## 162 ALose_v_Neut_L_Ins_r2~~ALose_v_Neut_L_Ins_r2       33         2  0.002
## 163 ALose_v_Neut_L_Ins_r2~~ALose_v_Neut_L_Ins_r2       33         3  0.001
## 164 ALose_v_Neut_L_Ins_r2~~ALose_v_Neut_L_Ins_r2       33         4 -0.003
## 165 ALose_v_Neut_L_Ins_r2~~ALose_v_Neut_L_Ins_r2       33         5 -0.004
## 166 ALose_v_Neut_R_Ins_r2~~ALose_v_Neut_R_Ins_r2       34         1 -0.001
## 167 ALose_v_Neut_R_Ins_r2~~ALose_v_Neut_R_Ins_r2       34         2  0.001
## 168 ALose_v_Neut_R_Ins_r2~~ALose_v_Neut_R_Ins_r2       34         3  0.000
## 169 ALose_v_Neut_R_Ins_r2~~ALose_v_Neut_R_Ins_r2       34         4  0.000
## 170 ALose_v_Neut_R_Ins_r2~~ALose_v_Neut_R_Ins_r2       34         5 -0.001
## 171 BLose_v_Neut_L_Ins_r2~~BLose_v_Neut_L_Ins_r2       35         1  0.004
## 172 BLose_v_Neut_L_Ins_r2~~BLose_v_Neut_L_Ins_r2       35         2  0.005
## 173 BLose_v_Neut_L_Ins_r2~~BLose_v_Neut_L_Ins_r2       35         3 -0.002
## 174 BLose_v_Neut_L_Ins_r2~~BLose_v_Neut_L_Ins_r2       35         4 -0.006
## 175 BLose_v_Neut_L_Ins_r2~~BLose_v_Neut_L_Ins_r2       35         5 -0.007
## 176 BLose_v_Neut_R_Ins_r2~~BLose_v_Neut_R_Ins_r2       36         1  0.000
## 177 BLose_v_Neut_R_Ins_r2~~BLose_v_Neut_R_Ins_r2       36         2  0.000
## 178 BLose_v_Neut_R_Ins_r2~~BLose_v_Neut_R_Ins_r2       36         3  0.001
## 179 BLose_v_Neut_R_Ins_r2~~BLose_v_Neut_R_Ins_r2       36         4 -0.001
## 180 BLose_v_Neut_R_Ins_r2~~BLose_v_Neut_R_Ins_r2       36         5 -0.001
## 181   AWin_v_Neut_L_NAc_r2~~AWin_v_Neut_L_NAc_r2       37         1  0.004
## 182   AWin_v_Neut_L_NAc_r2~~AWin_v_Neut_L_NAc_r2       37         2  0.002
## 183   AWin_v_Neut_L_NAc_r2~~AWin_v_Neut_L_NAc_r2       37         3  0.001
## 184   AWin_v_Neut_L_NAc_r2~~AWin_v_Neut_L_NAc_r2       37         4 -0.006
## 185   AWin_v_Neut_L_NAc_r2~~AWin_v_Neut_L_NAc_r2       37         5 -0.018
## 186   AWin_v_Neut_R_NAc_r2~~AWin_v_Neut_R_NAc_r2       38         1 -0.006
## 187   AWin_v_Neut_R_NAc_r2~~AWin_v_Neut_R_NAc_r2       38         2 -0.001
## 188   AWin_v_Neut_R_NAc_r2~~AWin_v_Neut_R_NAc_r2       38         3  0.005
## 189   AWin_v_Neut_R_NAc_r2~~AWin_v_Neut_R_NAc_r2       38         4 -0.002
## 190   AWin_v_Neut_R_NAc_r2~~AWin_v_Neut_R_NAc_r2       38         5 -0.007
## 191   BWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       39         1  0.007
## 192   BWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       39         2  0.005
## 193   BWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       39         3  0.001
## 194   BWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       39         4 -0.010
## 195   BWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       39         5 -0.027
## 196   BWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       40         1 -0.006
## 197   BWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       40         2 -0.004
## 198   BWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       40         3  0.007
## 199   BWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       40         4 -0.001
## 200   BWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       40         5 -0.003
## 201 BWin_v_BLose_L_NAc_r2~~BWin_v_BLose_L_NAc_r2       41         1 -0.003
## 202 BWin_v_BLose_L_NAc_r2~~BWin_v_BLose_L_NAc_r2       41         2  0.010
## 203 BWin_v_BLose_L_NAc_r2~~BWin_v_BLose_L_NAc_r2       41         3 -0.002
## 204 BWin_v_BLose_L_NAc_r2~~BWin_v_BLose_L_NAc_r2       41         4 -0.004
## 205 BWin_v_BLose_L_NAc_r2~~BWin_v_BLose_L_NAc_r2       41         5 -0.003
## 206 BWin_v_BLose_R_NAc_r2~~BWin_v_BLose_R_NAc_r2       42         1  0.003
## 207 BWin_v_BLose_R_NAc_r2~~BWin_v_BLose_R_NAc_r2       42         2  0.000
## 208 BWin_v_BLose_R_NAc_r2~~BWin_v_BLose_R_NAc_r2       42         3 -0.005
## 209 BWin_v_BLose_R_NAc_r2~~BWin_v_BLose_R_NAc_r2       42         4  0.005
## 210 BWin_v_BLose_R_NAc_r2~~BWin_v_BLose_R_NAc_r2       42         5  0.009
## 211   AWin_v_Neut_R_Ins_r1~~AWin_v_Neut_R_Ins_r1       43         1 -0.002
## 212   AWin_v_Neut_R_Ins_r1~~AWin_v_Neut_R_Ins_r1       43         2  0.001
## 213   AWin_v_Neut_R_Ins_r1~~AWin_v_Neut_R_Ins_r1       43         3  0.001
## 214   AWin_v_Neut_R_Ins_r1~~AWin_v_Neut_R_Ins_r1       43         4 -0.001
## 215   AWin_v_Neut_R_Ins_r1~~AWin_v_Neut_R_Ins_r1       43         5 -0.003
## 216   BWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       44         1 -0.004
## 217   BWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       44         2  0.001
## 218   BWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       44         3  0.003
## 219   BWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       44         4 -0.001
## 220   BWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       44         5 -0.004
## 221 ALose_v_Neut_L_Ins_r1~~ALose_v_Neut_L_Ins_r1       45         1  0.000
## 222 ALose_v_Neut_L_Ins_r1~~ALose_v_Neut_L_Ins_r1       45         2 -0.001
## 223 ALose_v_Neut_L_Ins_r1~~ALose_v_Neut_L_Ins_r1       45         3  0.001
## 224 ALose_v_Neut_L_Ins_r1~~ALose_v_Neut_L_Ins_r1       45         4  0.000
## 225 ALose_v_Neut_L_Ins_r1~~ALose_v_Neut_L_Ins_r1       45         5  0.000
## 226 ALose_v_Neut_R_Ins_r1~~ALose_v_Neut_R_Ins_r1       46         1  0.000
## 227 ALose_v_Neut_R_Ins_r1~~ALose_v_Neut_R_Ins_r1       46         2  0.001
## 228 ALose_v_Neut_R_Ins_r1~~ALose_v_Neut_R_Ins_r1       46         3  0.000
## 229 ALose_v_Neut_R_Ins_r1~~ALose_v_Neut_R_Ins_r1       46         4 -0.001
## 230 ALose_v_Neut_R_Ins_r1~~ALose_v_Neut_R_Ins_r1       46         5 -0.002
## 231 BLose_v_Neut_L_Ins_r1~~BLose_v_Neut_L_Ins_r1       47         1  0.005
## 232 BLose_v_Neut_L_Ins_r1~~BLose_v_Neut_L_Ins_r1       47         2 -0.002
## 233 BLose_v_Neut_L_Ins_r1~~BLose_v_Neut_L_Ins_r1       47         3  0.000
## 234 BLose_v_Neut_L_Ins_r1~~BLose_v_Neut_L_Ins_r1       47         4 -0.003
## 235 BLose_v_Neut_L_Ins_r1~~BLose_v_Neut_L_Ins_r1       47         5 -0.004
## 236 BLose_v_Neut_R_Ins_r1~~BLose_v_Neut_R_Ins_r1       48         1  0.000
## 237 BLose_v_Neut_R_Ins_r1~~BLose_v_Neut_R_Ins_r1       48         2  0.000
## 238 BLose_v_Neut_R_Ins_r1~~BLose_v_Neut_R_Ins_r1       48         3  0.000
## 239 BLose_v_Neut_R_Ins_r1~~BLose_v_Neut_R_Ins_r1       48         4  0.000
## 240 BLose_v_Neut_R_Ins_r1~~BLose_v_Neut_R_Ins_r1       48         5 -0.001
## 241   AWin_v_Neut_L_NAc_r1~~AWin_v_Neut_L_NAc_r1       49         1  0.006
## 242   AWin_v_Neut_L_NAc_r1~~AWin_v_Neut_L_NAc_r1       49         2  0.000
## 243   AWin_v_Neut_L_NAc_r1~~AWin_v_Neut_L_NAc_r1       49         3 -0.002
## 244   AWin_v_Neut_L_NAc_r1~~AWin_v_Neut_L_NAc_r1       49         4 -0.002
## 245   AWin_v_Neut_L_NAc_r1~~AWin_v_Neut_L_NAc_r1       49         5 -0.003
## 246   AWin_v_Neut_R_NAc_r1~~AWin_v_Neut_R_NAc_r1       50         1  0.003
## 247   AWin_v_Neut_R_NAc_r1~~AWin_v_Neut_R_NAc_r1       50         2  0.002
## 248   AWin_v_Neut_R_NAc_r1~~AWin_v_Neut_R_NAc_r1       50         3 -0.003
## 249   AWin_v_Neut_R_NAc_r1~~AWin_v_Neut_R_NAc_r1       50         4  0.000
## 250   AWin_v_Neut_R_NAc_r1~~AWin_v_Neut_R_NAc_r1       50         5 -0.002
## 251   BWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       51         1  0.009
## 252   BWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       51         2  0.006
## 253   BWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       51         3 -0.004
## 254   BWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       51         4 -0.006
## 255   BWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       51         5 -0.005
## 256   BWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       52         1 -0.001
## 257   BWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       52         2  0.006
## 258   BWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       52         3 -0.001
## 259   BWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       52         4 -0.004
## 260   BWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       52         5 -0.009
## 261 BWin_v_BLose_L_NAc_r1~~BWin_v_BLose_L_NAc_r1       53         1 -0.007
## 262 BWin_v_BLose_L_NAc_r1~~BWin_v_BLose_L_NAc_r1       53         2 -0.003
## 263 BWin_v_BLose_L_NAc_r1~~BWin_v_BLose_L_NAc_r1       53         3  0.003
## 264 BWin_v_BLose_L_NAc_r1~~BWin_v_BLose_L_NAc_r1       53         4  0.003
## 265 BWin_v_BLose_L_NAc_r1~~BWin_v_BLose_L_NAc_r1       53         5  0.002
## 266 BWin_v_BLose_R_NAc_r1~~BWin_v_BLose_R_NAc_r1       54         1  0.003
## 267 BWin_v_BLose_R_NAc_r1~~BWin_v_BLose_R_NAc_r1       54         2 -0.003
## 268 BWin_v_BLose_R_NAc_r1~~BWin_v_BLose_R_NAc_r1       54         3  0.005
## 269 BWin_v_BLose_R_NAc_r1~~BWin_v_BLose_R_NAc_r1       54         4 -0.006
## 270 BWin_v_BLose_R_NAc_r1~~BWin_v_BLose_R_NAc_r1       54         5 -0.015
## 271             Avoid_Insula_r2~~Avoid_Insula_r2       55         1  0.000
## 272             Avoid_Insula_r2~~Avoid_Insula_r2       55         2  0.000
## 273             Avoid_Insula_r2~~Avoid_Insula_r2       55         3  0.000
## 274             Avoid_Insula_r2~~Avoid_Insula_r2       55         4  0.000
## 275             Avoid_Insula_r2~~Avoid_Insula_r2       55         5  0.000
## 276                   Appr_NAcc_r2~~Appr_NAcc_r2       56         1  0.000
## 277                   Appr_NAcc_r2~~Appr_NAcc_r2       56         2  0.000
## 278                   Appr_NAcc_r2~~Appr_NAcc_r2       56         3  0.000
## 279                   Appr_NAcc_r2~~Appr_NAcc_r2       56         4  0.000
## 280                   Appr_NAcc_r2~~Appr_NAcc_r2       56         5  0.000
## 281             Avoid_Insula_r1~~Avoid_Insula_r1       57         1  0.000
## 282             Avoid_Insula_r1~~Avoid_Insula_r1       57         2  0.000
## 283             Avoid_Insula_r1~~Avoid_Insula_r1       57         3  0.000
## 284             Avoid_Insula_r1~~Avoid_Insula_r1       57         4  0.000
## 285             Avoid_Insula_r1~~Avoid_Insula_r1       57         5  0.000
## 286                   Appr_NAcc_r1~~Appr_NAcc_r1       58         1  0.000
## 287                   Appr_NAcc_r1~~Appr_NAcc_r1       58         2  0.000
## 288                   Appr_NAcc_r1~~Appr_NAcc_r1       58         3  0.000
## 289                   Appr_NAcc_r1~~Appr_NAcc_r1       58         4  0.000
## 290                   Appr_NAcc_r1~~Appr_NAcc_r1       58         5  0.000
## 291                Avoid_Insula_r2~~Appr_NAcc_r2       59         1 -0.041
## 292                Avoid_Insula_r2~~Appr_NAcc_r2       59         2 -0.016
## 293                Avoid_Insula_r2~~Appr_NAcc_r2       59         3 -0.090
## 294                Avoid_Insula_r2~~Appr_NAcc_r2       59         4  0.160
## 295                Avoid_Insula_r2~~Appr_NAcc_r2       59         5  0.253
## 296             Avoid_Insula_r2~~Avoid_Insula_r1       60         1  0.035
## 297             Avoid_Insula_r2~~Avoid_Insula_r1       60         2  0.039
## 298             Avoid_Insula_r2~~Avoid_Insula_r1       60         3 -0.008
## 299             Avoid_Insula_r2~~Avoid_Insula_r1       60         4 -0.049
## 300             Avoid_Insula_r2~~Avoid_Insula_r1       60         5 -0.040
## 301                Avoid_Insula_r2~~Appr_NAcc_r1       61         1 -0.021
## 302                Avoid_Insula_r2~~Appr_NAcc_r1       61         2 -0.005
## 303                Avoid_Insula_r2~~Appr_NAcc_r1       61         3  0.017
## 304                Avoid_Insula_r2~~Appr_NAcc_r1       61         4 -0.003
## 305                Avoid_Insula_r2~~Appr_NAcc_r1       61         5 -0.016
## 306                Appr_NAcc_r2~~Avoid_Insula_r1       62         1 -0.111
## 307                Appr_NAcc_r2~~Avoid_Insula_r1       62         2  0.018
## 308                Appr_NAcc_r2~~Avoid_Insula_r1       62         3  0.037
## 309                Appr_NAcc_r2~~Avoid_Insula_r1       62         4  0.012
## 310                Appr_NAcc_r2~~Avoid_Insula_r1       62         5  0.023
## 311                   Appr_NAcc_r2~~Appr_NAcc_r1       63         1 -0.051
## 312                   Appr_NAcc_r2~~Appr_NAcc_r1       63         2 -0.008
## 313                   Appr_NAcc_r2~~Appr_NAcc_r1       63         3 -0.014
## 314                   Appr_NAcc_r2~~Appr_NAcc_r1       63         4  0.059
## 315                   Appr_NAcc_r2~~Appr_NAcc_r1       63         5  0.147
## 316                Avoid_Insula_r1~~Appr_NAcc_r1       64         1 -0.134
## 317                Avoid_Insula_r1~~Appr_NAcc_r1       64         2 -0.167
## 318                Avoid_Insula_r1~~Appr_NAcc_r1       64         3  0.095
## 319                Avoid_Insula_r1~~Appr_NAcc_r1       64         4  0.119
## 320                Avoid_Insula_r1~~Appr_NAcc_r1       64         5  0.114
## 321                                        rmsea       65         1  0.002
## 322                                        rmsea       65         2  0.002
## 323                                        rmsea       65         3  0.004
## 324                                        rmsea       65         4 -0.007
## 325                                        rmsea       65         5 -0.145
## 326                                          cfi       66         1 -0.001
## 327                                          cfi       66         2 -0.006
## 328                                          cfi       66         3 -0.010
## 329                                          cfi       66         4  0.016
## 330                                          cfi       66         5  0.218
## 331                                          tli       67         1 -0.001
## 332                                          tli       67         2 -0.007
## 333                                          tli       67         3 -0.011
## 334                                          tli       67         4  0.018
## 335                                          tli       67         5  0.305
## 336                                          gfi       68         1 -0.037
## 337                                          gfi       68         2 -0.004
## 338                                          gfi       68         3  0.013
## 339                                          gfi       68         4  0.013
## 340                                          gfi       68         5 -0.031
## 341                                         srmr       69         1  0.010
## 342                                         srmr       69         2  0.007
## 343                                         srmr       69         3  0.002
## 344                                         srmr       69         4 -0.016
## 345                                         srmr       69         5 -0.011
##         p
## 1   0.464
## 2   0.778
## 3   0.836
## 4   0.484
## 5   0.164
## 6   0.200
## 7   0.640
## 8   0.416
## 9   0.422
## 10  0.396
## 11  0.612
## 12  0.202
## 13  0.512
## 14  0.028
## 15  0.006
## 16  0.274
## 17  0.578
## 18  0.456
## 19  0.014
## 20  0.008
## 21  0.996
## 22  0.074
## 23  0.622
## 24  0.096
## 25  0.078
## 26  0.420
## 27  0.480
## 28  0.538
## 29  0.064
## 30  0.078
## 31  0.982
## 32  0.566
## 33  0.090
## 34  0.082
## 35  0.024
## 36  0.696
## 37  0.224
## 38  0.096
## 39  0.924
## 40  0.614
## 41  0.882
## 42  0.502
## 43  0.062
## 44  0.074
## 45  0.018
## 46  0.716
## 47  0.050
## 48  0.218
## 49  0.492
## 50  0.590
## 51  0.944
## 52  0.778
## 53  0.368
## 54  0.294
## 55  0.152
## 56  0.822
## 57  0.024
## 58  0.200
## 59  0.010
## 60  0.032
## 61  0.026
## 62  0.580
## 63  0.076
## 64  0.838
## 65  0.994
## 66  0.194
## 67  0.144
## 68  0.202
## 69  0.434
## 70  0.358
## 71  0.802
## 72  0.112
## 73  0.876
## 74  0.124
## 75  0.396
## 76  0.680
## 77  0.262
## 78  0.396
## 79  0.584
## 80  0.998
## 81  0.662
## 82  0.906
## 83  0.758
## 84  0.820
## 85  0.596
## 86  0.328
## 87  0.670
## 88  0.048
## 89  0.268
## 90  0.076
## 91  0.268
## 92  0.452
## 93  0.592
## 94  0.282
## 95  0.446
## 96  0.404
## 97  0.210
## 98  0.596
## 99  0.196
## 100 0.258
## 101 0.176
## 102 0.500
## 103 0.380
## 104 0.302
## 105 0.568
## 106 0.532
## 107 0.278
## 108 0.958
## 109 0.184
## 110 0.146
## 111 0.372
## 112 0.180
## 113 0.636
## 114 0.140
## 115 0.164
## 116 0.052
## 117 0.434
## 118 0.200
## 119 0.236
## 120 0.364
## 121 0.498
## 122 0.662
## 123 0.590
## 124 0.632
## 125 0.734
## 126 0.616
## 127 0.500
## 128 0.544
## 129 0.160
## 130 0.016
## 131 0.752
## 132 0.318
## 133 0.540
## 134 0.662
## 135 0.476
## 136 0.490
## 137 0.608
## 138 0.116
## 139 0.690
## 140 0.540
## 141 0.432
## 142 0.888
## 143 0.216
## 144 0.700
## 145 0.316
## 146 0.690
## 147 0.294
## 148 0.104
## 149 0.834
## 150 0.354
## 151 0.622
## 152 0.346
## 153 0.080
## 154 0.730
## 155 0.218
## 156 0.734
## 157 0.248
## 158 0.136
## 159 0.886
## 160 0.542
## 161 0.962
## 162 0.122
## 163 0.712
## 164 0.206
## 165 0.306
## 166 0.382
## 167 0.198
## 168 0.994
## 169 0.932
## 170 0.690
## 171 0.244
## 172 0.026
## 173 0.366
## 174 0.044
## 175 0.112
## 176 0.890
## 177 0.928
## 178 0.292
## 179 0.608
## 180 0.778
## 181 0.508
## 182 0.656
## 183 0.718
## 184 0.282
## 185 0.040
## 186 0.510
## 187 0.804
## 188 0.148
## 189 0.638
## 190 0.412
## 191 0.342
## 192 0.300
## 193 0.766
## 194 0.058
## 195 0.014
## 196 0.546
## 197 0.408
## 198 0.148
## 199 0.878
## 200 0.812
## 201 0.736
## 202 0.024
## 203 0.500
## 204 0.458
## 205 0.784
## 206 0.652
## 207 0.986
## 208 0.068
## 209 0.242
## 210 0.204
## 211 0.496
## 212 0.632
## 213 0.242
## 214 0.566
## 215 0.188
## 216 0.330
## 217 0.800
## 218 0.178
## 219 0.736
## 220 0.464
## 221 0.992
## 222 0.610
## 223 0.614
## 224 0.962
## 225 0.826
## 226 0.964
## 227 0.280
## 228 0.594
## 229 0.268
## 230 0.148
## 231 0.128
## 232 0.436
## 233 0.860
## 234 0.304
## 235 0.382
## 236 0.958
## 237 0.634
## 238 0.872
## 239 0.762
## 240 0.712
## 241 0.464
## 242 0.962
## 243 0.642
## 244 0.758
## 245 0.786
## 246 0.606
## 247 0.660
## 248 0.406
## 249 0.978
## 250 0.870
## 251 0.474
## 252 0.460
## 253 0.466
## 254 0.516
## 255 0.670
## 256 0.972
## 257 0.240
## 258 0.916
## 259 0.596
## 260 0.296
## 261 0.398
## 262 0.474
## 263 0.444
## 264 0.578
## 265 0.736
## 266 0.590
## 267 0.680
## 268 0.400
## 269 0.504
## 270 0.196
## 271 1.000
## 272 1.000
## 273 1.000
## 274 1.000
## 275 1.000
## 276 1.000
## 277 1.000
## 278 1.000
## 279 1.000
## 280 1.000
## 281 1.000
## 282 1.000
## 283 1.000
## 284 1.000
## 285 1.000
## 286 1.000
## 287 1.000
## 288 1.000
## 289 1.000
## 290 1.000
## 291 0.744
## 292 0.872
## 293 0.128
## 294 0.088
## 295 0.094
## 296 0.730
## 297 0.522
## 298 0.866
## 299 0.534
## 300 0.722
## 301 0.868
## 302 0.942
## 303 0.744
## 304 0.982
## 305 0.914
## 306 0.338
## 307 0.844
## 308 0.504
## 309 0.804
## 310 0.792
## 311 0.672
## 312 0.840
## 313 0.806
## 314 0.514
## 315 0.256
## 316 0.406
## 317 0.070
## 318 0.196
## 319 0.298
## 320 0.460
## 321 0.066
## 322 0.092
## 323 0.000
## 324 0.032
## 325 0.000
## 326 0.076
## 327 0.162
## 328 0.006
## 329 0.052
## 330 0.000
## 331 0.076
## 332 0.158
## 333 0.006
## 334 0.060
## 335 0.000
## 336 0.638
## 337 0.256
## 338 0.928
## 339 0.156
## 340 0.300
## 341 0.842
## 342 0.294
## 343 0.430
## 344 0.084
## 345 0.088

8.4.2 youth

plot(lsem.permuted_yth,type = "global",title = "Global Statistics for Youth PDS")

summary(lsem.permuted_yth) # examine results

## -----------------------------------------------------------------
## Permutation Test for Local Structural Equation Model 
## 
## sirt 3.12-66 (2022-05-16 12:27:54) 
## lavaan 0.6-12 (2022-07-04 16:40:02 UTC) 
## 
## Function 'sirt::lsem.permutationTest' 
## 
## 
## Call:
## sirt::lsem.permutationTest(lsem.object = lsem.MID_yth, B = n_permutations, 
##     residualize = FALSE)
## 
## Date of Analysis: 2023-11-27 13:20:49 
## Time difference of 57.90787 mins
## Computation Time: 57.90787 
## 
## Number of permutations = 1000 
## Percentage of non-converged datasets = 10.794 
## Number of observations=343 
## Bandwidth factor=2 
## Bandwidth=0.618 
## Number of focal points for moderator=5 
## 
## lavaan Model
## 
## # Factor loadings
## Avoid_Insula_r2 =~ AWin_v_Neut_R_Ins_r2 + BWin_v_Neut_R_Ins_r2 + ALose_v_Neut_L_Ins_r2 + ALose_v_Neut_R_Ins_r2 + BLose_v_Neut_L_Ins_r2 + ALose_v_Neut_R_Ins_r2*BLose_v_Neut_R_Ins_r2
## 
## Appr_NAcc_r2 =~ AWin_v_Neut_L_NAc_r2 + AWin_v_Neut_R_NAc_r2 + BWin_v_Neut_L_NAc_r2 +
##         AWin_v_Neut_R_NAc_r2*BWin_v_Neut_R_NAc_r2 + BWin_v_BLose_L_NAc_r2 + BWin_v_BLose_R_NAc_r2
## 
## Avoid_Insula_r1 =~ AWin_v_Neut_R_Ins_r1 + BWin_v_Neut_R_Ins_r1 + ALose_v_Neut_L_Ins_r1 + ALose_v_Neut_R_Ins_r1 
##           + BLose_v_Neut_L_Ins_r1 + ALose_v_Neut_R_Ins_r1*BLose_v_Neut_R_Ins_r1
## 
## Appr_NAcc_r1 =~ AWin_v_Neut_L_NAc_r1 + AWin_v_Neut_R_NAc_r1 + AWin_v_Neut_L_NAc_r1*BWin_v_Neut_L_NAc_r1 + 
##         BWin_v_Neut_R_NAc_r1 + BWin_v_BLose_L_NAc_r1 + BWin_v_BLose_R_NAc_r1
## 
## 
## ## Correlated residuals
## ## Nacc
## AWin_v_Neut_L_NAc_r1 ~~  BWin_v_Neut_L_NAc_r1
## AWin_v_Neut_L_NAc_r2 ~~  BWin_v_Neut_L_NAc_r2 
## AWin_v_Neut_R_NAc_r1 ~~  BWin_v_Neut_R_NAc_r1 
## AWin_v_Neut_R_NAc_r2 ~~  BWin_v_Neut_R_NAc_r2
## ## Insula
## AWin_v_Neut_R_Ins_r1 ~~  BWin_v_Neut_R_Ins_r1
## AWin_v_Neut_R_Ins_r2 ~~  BWin_v_Neut_R_Ins_r2
## 
## 
## Global Test Statistics
## 
##                                             par      M    SD  SD_p   MAD MAD_p
## 1         Avoid_Insula_r2=~AWin_v_Neut_R_Ins_r2  0.133 0.016 0.230 0.013 0.245
## 2         Avoid_Insula_r2=~BWin_v_Neut_R_Ins_r2  0.132 0.022 0.126 0.017 0.161
## 3        Avoid_Insula_r2=~ALose_v_Neut_L_Ins_r2  0.111 0.023 0.028 0.020 0.026
## 4        Avoid_Insula_r2=~ALose_v_Neut_R_Ins_r2  0.177 0.024 0.018 0.020 0.020
## 5        Avoid_Insula_r2=~BLose_v_Neut_L_Ins_r2  0.119 0.015 0.272 0.011 0.330
## 6        Avoid_Insula_r2=~BLose_v_Neut_R_Ins_r2  0.194 0.019 0.048 0.016 0.059
## 7            Appr_NAcc_r2=~AWin_v_Neut_L_NAc_r2  0.107 0.024 0.252 0.019 0.291
## 8            Appr_NAcc_r2=~AWin_v_Neut_R_NAc_r2  0.114 0.009 0.952 0.008 0.914
## 9            Appr_NAcc_r2=~BWin_v_Neut_L_NAc_r2  0.181 0.021 0.299 0.017 0.326
## 10           Appr_NAcc_r2=~BWin_v_Neut_R_NAc_r2  0.183 0.006 0.981 0.005 0.979
## 11          Appr_NAcc_r2=~BWin_v_BLose_L_NAc_r2  0.170 0.014 0.566 0.010 0.619
## 12          Appr_NAcc_r2=~BWin_v_BLose_R_NAc_r2  0.172 0.028 0.088 0.023 0.090
## 13        Avoid_Insula_r1=~AWin_v_Neut_R_Ins_r1  0.113 0.003 0.971 0.003 0.960
## 14        Avoid_Insula_r1=~BWin_v_Neut_R_Ins_r1  0.120 0.009 0.713 0.008 0.640
## 15       Avoid_Insula_r1=~ALose_v_Neut_L_Ins_r1  0.116 0.009 0.553 0.007 0.546
## 16       Avoid_Insula_r1=~ALose_v_Neut_R_Ins_r1  0.169 0.010 0.311 0.007 0.474
## 17       Avoid_Insula_r1=~BLose_v_Neut_L_Ins_r1  0.136 0.009 0.669 0.007 0.655
## 18       Avoid_Insula_r1=~BLose_v_Neut_R_Ins_r1  0.189 0.017 0.090 0.015 0.050
## 19           Appr_NAcc_r1=~AWin_v_Neut_L_NAc_r1  0.125 0.018 0.625 0.017 0.530
## 20           Appr_NAcc_r1=~AWin_v_Neut_R_NAc_r1  0.117 0.014 0.742 0.013 0.650
## 21           Appr_NAcc_r1=~BWin_v_Neut_L_NAc_r1  0.193 0.021 0.523 0.020 0.390
## 22           Appr_NAcc_r1=~BWin_v_Neut_R_NAc_r1  0.173 0.011 0.870 0.010 0.775
## 23          Appr_NAcc_r1=~BWin_v_BLose_L_NAc_r1  0.169 0.018 0.518 0.014 0.563
## 24          Appr_NAcc_r1=~BWin_v_BLose_R_NAc_r1  0.150 0.032 0.188 0.028 0.154
## 25   AWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1  0.034 0.005 0.651 0.005 0.504
## 26   AWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2  0.032 0.004 0.536 0.002 0.857
## 27   AWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1  0.031 0.003 0.847 0.002 0.793
## 28   AWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2  0.033 0.004 0.672 0.004 0.561
## 29   AWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1  0.016 0.002 0.455 0.002 0.352
## 30   AWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2  0.024 0.001 0.997 0.000 0.998
## 31   AWin_v_Neut_R_Ins_r2~~AWin_v_Neut_R_Ins_r2  0.022 0.001 0.991 0.000 0.986
## 32   BWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2  0.038 0.002 0.932 0.001 0.935
## 33 ALose_v_Neut_L_Ins_r2~~ALose_v_Neut_L_Ins_r2  0.017 0.002 0.622 0.001 0.660
## 34 ALose_v_Neut_R_Ins_r2~~ALose_v_Neut_R_Ins_r2  0.004 0.000 0.977 0.000 0.983
## 35 BLose_v_Neut_L_Ins_r2~~BLose_v_Neut_L_Ins_r2  0.022 0.003 0.252 0.002 0.291
## 36 BLose_v_Neut_R_Ins_r2~~BLose_v_Neut_R_Ins_r2  0.006 0.001 0.778 0.001 0.706
## 37   AWin_v_Neut_L_NAc_r2~~AWin_v_Neut_L_NAc_r2  0.037 0.004 0.655 0.002 0.851
## 38   AWin_v_Neut_R_NAc_r2~~AWin_v_Neut_R_NAc_r2  0.038 0.003 0.812 0.003 0.705
## 39   BWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2  0.037 0.006 0.354 0.004 0.573
## 40   BWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2  0.038 0.004 0.706 0.004 0.629
## 41 BWin_v_BLose_L_NAc_r2~~BWin_v_BLose_L_NAc_r2  0.026 0.004 0.564 0.003 0.576
## 42 BWin_v_BLose_R_NAc_r2~~BWin_v_BLose_R_NAc_r2  0.030 0.004 0.469 0.004 0.365
## 43   AWin_v_Neut_R_Ins_r1~~AWin_v_Neut_R_Ins_r1  0.016 0.002 0.399 0.001 0.308
## 44   BWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1  0.026 0.002 0.596 0.002 0.550
## 45 ALose_v_Neut_L_Ins_r1~~ALose_v_Neut_L_Ins_r1  0.014 0.001 0.870 0.001 0.861
## 46 ALose_v_Neut_R_Ins_r1~~ALose_v_Neut_R_Ins_r1  0.003 0.001 0.668 0.000 0.689
## 47 BLose_v_Neut_L_Ins_r1~~BLose_v_Neut_L_Ins_r1  0.018 0.002 0.461 0.002 0.429
## 48 BLose_v_Neut_R_Ins_r1~~BLose_v_Neut_R_Ins_r1  0.007 0.001 0.648 0.001 0.556
## 49   AWin_v_Neut_L_NAc_r1~~AWin_v_Neut_L_NAc_r1  0.040 0.003 0.868 0.003 0.747
## 50   AWin_v_Neut_R_NAc_r1~~AWin_v_Neut_R_NAc_r1  0.036 0.002 0.925 0.002 0.877
## 51   BWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1  0.036 0.007 0.473 0.007 0.317
## 52   BWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1  0.036 0.003 0.793 0.003 0.752
## 53 BWin_v_BLose_L_NAc_r1~~BWin_v_BLose_L_NAc_r1  0.024 0.002 0.969 0.001 0.930
## 54 BWin_v_BLose_R_NAc_r1~~BWin_v_BLose_R_NAc_r1  0.041 0.008 0.314 0.005 0.553
## 55             Avoid_Insula_r2~~Avoid_Insula_r2  1.000 0.000 1.000 0.000 1.000
## 56                   Appr_NAcc_r2~~Appr_NAcc_r2  1.000 0.000 1.000 0.000 1.000
## 57             Avoid_Insula_r1~~Avoid_Insula_r1  1.000 0.000 1.000 0.000 1.000
## 58                   Appr_NAcc_r1~~Appr_NAcc_r1  1.000 0.000 1.000 0.000 1.000
## 59                Avoid_Insula_r2~~Appr_NAcc_r2  0.032 0.100 0.239 0.089 0.188
## 60             Avoid_Insula_r2~~Avoid_Insula_r1  0.006 0.051 0.644 0.049 0.504
## 61                Avoid_Insula_r2~~Appr_NAcc_r1  0.025 0.079 0.325 0.066 0.307
## 62                Appr_NAcc_r2~~Avoid_Insula_r1  0.058 0.057 0.615 0.051 0.518
## 63                   Appr_NAcc_r2~~Appr_NAcc_r1  0.164 0.042 0.900 0.033 0.893
## 64                Avoid_Insula_r1~~Appr_NAcc_r1 -0.009 0.071 0.742 0.060 0.692
## 65                                        rmsea  0.145 0.014 0.000 0.007 0.315
## 66                                          cfi  0.781 0.028 0.046 0.015 0.476
## 67                                          tli  0.748 0.032 0.046 0.017 0.476
## 68                                          gfi  0.690 0.027 0.209 0.019 0.371
## 69                                         srmr  0.120 0.010 0.457 0.007 0.595
##    lin_slo lin_slo_p
## 1   -0.015     0.130
## 2   -0.021     0.082
## 3   -0.023     0.012
## 4   -0.024     0.012
## 5   -0.015     0.122
## 6   -0.017     0.032
## 7    0.021     0.168
## 8    0.003     0.894
## 9    0.018     0.222
## 10   0.001     0.956
## 11  -0.011     0.400
## 12  -0.016     0.234
## 13   0.000     0.988
## 14   0.009     0.380
## 15   0.008     0.356
## 16   0.005     0.502
## 17  -0.008     0.348
## 18  -0.003     0.736
## 19   0.014     0.400
## 20   0.008     0.598
## 21   0.017     0.362
## 22   0.008     0.636
## 23  -0.015     0.312
## 24  -0.032     0.082
## 25  -0.004     0.380
## 26  -0.002     0.676
## 27  -0.002     0.616
## 28   0.000     0.982
## 29   0.000     0.928
## 30  -0.001     0.788
## 31   0.000     0.920
## 32   0.000     0.912
## 33  -0.001     0.358
## 34   0.000     0.856
## 35  -0.002     0.178
## 36   0.000     0.882
## 37  -0.001     0.816
## 38   0.000     0.980
## 39  -0.004     0.348
## 40   0.000     0.938
## 41  -0.003     0.388
## 42   0.001     0.812
## 43   0.000     0.940
## 44  -0.001     0.502
## 45   0.000     0.868
## 46  -0.001     0.316
## 47  -0.002     0.226
## 48   0.000     0.978
## 49  -0.002     0.542
## 50   0.000     0.896
## 51  -0.006     0.266
## 52  -0.002     0.562
## 53   0.000     0.970
## 54  -0.007     0.170
## 55   0.000     1.000
## 56   0.000     1.000
## 57   0.000     1.000
## 58   0.000     1.000
## 59   0.025     0.676
## 60   0.002     0.964
## 61  -0.073     0.150
## 62  -0.040     0.444
## 63   0.024     0.758
## 64   0.051     0.512
## 65  -0.008     0.004
## 66   0.016     0.054
## 67   0.018     0.054
## 68   0.012     0.238
## 69  -0.008     0.294
## 
## Pointwise Test Statistics
## 
##                                              par parindex moderator    est
## 1          Avoid_Insula_r2=~AWin_v_Neut_R_Ins_r2        1         1  0.035
## 2          Avoid_Insula_r2=~AWin_v_Neut_R_Ins_r2        1         2  0.008
## 3          Avoid_Insula_r2=~AWin_v_Neut_R_Ins_r2        1         3 -0.006
## 4          Avoid_Insula_r2=~AWin_v_Neut_R_Ins_r2        1         4 -0.017
## 5          Avoid_Insula_r2=~AWin_v_Neut_R_Ins_r2        1         5 -0.013
## 6          Avoid_Insula_r2=~BWin_v_Neut_R_Ins_r2        2         1  0.052
## 7          Avoid_Insula_r2=~BWin_v_Neut_R_Ins_r2        2         2  0.010
## 8          Avoid_Insula_r2=~BWin_v_Neut_R_Ins_r2        2         3 -0.009
## 9          Avoid_Insula_r2=~BWin_v_Neut_R_Ins_r2        2         4 -0.023
## 10         Avoid_Insula_r2=~BWin_v_Neut_R_Ins_r2        2         5 -0.015
## 11        Avoid_Insula_r2=~ALose_v_Neut_L_Ins_r2        3         1  0.047
## 12        Avoid_Insula_r2=~ALose_v_Neut_L_Ins_r2        3         2  0.017
## 13        Avoid_Insula_r2=~ALose_v_Neut_L_Ins_r2        3         3 -0.012
## 14        Avoid_Insula_r2=~ALose_v_Neut_L_Ins_r2        3         4 -0.021
## 15        Avoid_Insula_r2=~ALose_v_Neut_L_Ins_r2        3         5 -0.051
## 16        Avoid_Insula_r2=~ALose_v_Neut_R_Ins_r2        4         1  0.032
## 17        Avoid_Insula_r2=~ALose_v_Neut_R_Ins_r2        4         2  0.022
## 18        Avoid_Insula_r2=~ALose_v_Neut_R_Ins_r2        4         3 -0.003
## 19        Avoid_Insula_r2=~ALose_v_Neut_R_Ins_r2        4         4 -0.035
## 20        Avoid_Insula_r2=~ALose_v_Neut_R_Ins_r2        4         5 -0.050
## 21        Avoid_Insula_r2=~BLose_v_Neut_L_Ins_r2        5         1  0.027
## 22        Avoid_Insula_r2=~BLose_v_Neut_L_Ins_r2        5         2  0.009
## 23        Avoid_Insula_r2=~BLose_v_Neut_L_Ins_r2        5         3 -0.003
## 24        Avoid_Insula_r2=~BLose_v_Neut_L_Ins_r2        5         4 -0.016
## 25        Avoid_Insula_r2=~BLose_v_Neut_L_Ins_r2        5         5 -0.050
## 26        Avoid_Insula_r2=~BLose_v_Neut_R_Ins_r2        6         1  0.012
## 27        Avoid_Insula_r2=~BLose_v_Neut_R_Ins_r2        6         2  0.018
## 28        Avoid_Insula_r2=~BLose_v_Neut_R_Ins_r2        6         3  0.004
## 29        Avoid_Insula_r2=~BLose_v_Neut_R_Ins_r2        6         4 -0.032
## 30        Avoid_Insula_r2=~BLose_v_Neut_R_Ins_r2        6         5 -0.046
## 31            Appr_NAcc_r2=~AWin_v_Neut_L_NAc_r2        7         1 -0.017
## 32            Appr_NAcc_r2=~AWin_v_Neut_L_NAc_r2        7         2 -0.020
## 33            Appr_NAcc_r2=~AWin_v_Neut_L_NAc_r2        7         3 -0.005
## 34            Appr_NAcc_r2=~AWin_v_Neut_L_NAc_r2        7         4  0.034
## 35            Appr_NAcc_r2=~AWin_v_Neut_L_NAc_r2        7         5  0.086
## 36            Appr_NAcc_r2=~AWin_v_Neut_R_NAc_r2        8         1  0.011
## 37            Appr_NAcc_r2=~AWin_v_Neut_R_NAc_r2        8         2 -0.006
## 38            Appr_NAcc_r2=~AWin_v_Neut_R_NAc_r2        8         3 -0.006
## 39            Appr_NAcc_r2=~AWin_v_Neut_R_NAc_r2        8         4  0.009
## 40            Appr_NAcc_r2=~AWin_v_Neut_R_NAc_r2        8         5  0.036
## 41            Appr_NAcc_r2=~BWin_v_Neut_L_NAc_r2        9         1 -0.011
## 42            Appr_NAcc_r2=~BWin_v_Neut_L_NAc_r2        9         2 -0.017
## 43            Appr_NAcc_r2=~BWin_v_Neut_L_NAc_r2        9         3 -0.006
## 44            Appr_NAcc_r2=~BWin_v_Neut_L_NAc_r2        9         4  0.031
## 45            Appr_NAcc_r2=~BWin_v_Neut_L_NAc_r2        9         5  0.071
## 46            Appr_NAcc_r2=~BWin_v_Neut_R_NAc_r2       10         1  0.001
## 47            Appr_NAcc_r2=~BWin_v_Neut_R_NAc_r2       10         2 -0.008
## 48            Appr_NAcc_r2=~BWin_v_Neut_R_NAc_r2       10         3  0.006
## 49            Appr_NAcc_r2=~BWin_v_Neut_R_NAc_r2       10         4  0.000
## 50            Appr_NAcc_r2=~BWin_v_Neut_R_NAc_r2       10         5 -0.015
## 51           Appr_NAcc_r2=~BWin_v_BLose_L_NAc_r2       11         1  0.004
## 52           Appr_NAcc_r2=~BWin_v_BLose_L_NAc_r2       11         2  0.012
## 53           Appr_NAcc_r2=~BWin_v_BLose_L_NAc_r2       11         3  0.004
## 54           Appr_NAcc_r2=~BWin_v_BLose_L_NAc_r2       11         4 -0.017
## 55           Appr_NAcc_r2=~BWin_v_BLose_L_NAc_r2       11         5 -0.062
## 56           Appr_NAcc_r2=~BWin_v_BLose_R_NAc_r2       12         1 -0.011
## 57           Appr_NAcc_r2=~BWin_v_BLose_R_NAc_r2       12         2  0.018
## 58           Appr_NAcc_r2=~BWin_v_BLose_R_NAc_r2       12         3  0.018
## 59           Appr_NAcc_r2=~BWin_v_BLose_R_NAc_r2       12         4 -0.037
## 60           Appr_NAcc_r2=~BWin_v_BLose_R_NAc_r2       12         5 -0.108
## 61         Avoid_Insula_r1=~AWin_v_Neut_R_Ins_r1       13         1 -0.003
## 62         Avoid_Insula_r1=~AWin_v_Neut_R_Ins_r1       13         2 -0.001
## 63         Avoid_Insula_r1=~AWin_v_Neut_R_Ins_r1       13         3  0.004
## 64         Avoid_Insula_r1=~AWin_v_Neut_R_Ins_r1       13         4 -0.002
## 65         Avoid_Insula_r1=~AWin_v_Neut_R_Ins_r1       13         5 -0.012
## 66         Avoid_Insula_r1=~BWin_v_Neut_R_Ins_r1       14         1 -0.016
## 67         Avoid_Insula_r1=~BWin_v_Neut_R_Ins_r1       14         2 -0.008
## 68         Avoid_Insula_r1=~BWin_v_Neut_R_Ins_r1       14         3  0.003
## 69         Avoid_Insula_r1=~BWin_v_Neut_R_Ins_r1       14         4  0.011
## 70         Avoid_Insula_r1=~BWin_v_Neut_R_Ins_r1       14         5  0.010
## 71        Avoid_Insula_r1=~ALose_v_Neut_L_Ins_r1       15         1 -0.007
## 72        Avoid_Insula_r1=~ALose_v_Neut_L_Ins_r1       15         2 -0.010
## 73        Avoid_Insula_r1=~ALose_v_Neut_L_Ins_r1       15         3  0.001
## 74        Avoid_Insula_r1=~ALose_v_Neut_L_Ins_r1       15         4  0.014
## 75        Avoid_Insula_r1=~ALose_v_Neut_L_Ins_r1       15         5  0.000
## 76        Avoid_Insula_r1=~ALose_v_Neut_R_Ins_r1       16         1 -0.025
## 77        Avoid_Insula_r1=~ALose_v_Neut_R_Ins_r1       16         2  0.002
## 78        Avoid_Insula_r1=~ALose_v_Neut_R_Ins_r1       16         3  0.007
## 79        Avoid_Insula_r1=~ALose_v_Neut_R_Ins_r1       16         4  0.002
## 80        Avoid_Insula_r1=~ALose_v_Neut_R_Ins_r1       16         5 -0.022
## 81        Avoid_Insula_r1=~BLose_v_Neut_L_Ins_r1       17         1  0.021
## 82        Avoid_Insula_r1=~BLose_v_Neut_L_Ins_r1       17         2  0.005
## 83        Avoid_Insula_r1=~BLose_v_Neut_L_Ins_r1       17         3 -0.005
## 84        Avoid_Insula_r1=~BLose_v_Neut_L_Ins_r1       17         4 -0.006
## 85        Avoid_Insula_r1=~BLose_v_Neut_L_Ins_r1       17         5 -0.021
## 86        Avoid_Insula_r1=~BLose_v_Neut_R_Ins_r1       18         1 -0.029
## 87        Avoid_Insula_r1=~BLose_v_Neut_R_Ins_r1       18         2  0.013
## 88        Avoid_Insula_r1=~BLose_v_Neut_R_Ins_r1       18         3  0.011
## 89        Avoid_Insula_r1=~BLose_v_Neut_R_Ins_r1       18         4 -0.017
## 90        Avoid_Insula_r1=~BLose_v_Neut_R_Ins_r1       18         5 -0.039
## 91            Appr_NAcc_r1=~AWin_v_Neut_L_NAc_r1       19         1 -0.036
## 92            Appr_NAcc_r1=~AWin_v_Neut_L_NAc_r1       19         2 -0.014
## 93            Appr_NAcc_r1=~AWin_v_Neut_L_NAc_r1       19         3  0.017
## 94            Appr_NAcc_r1=~AWin_v_Neut_L_NAc_r1       19         4  0.011
## 95            Appr_NAcc_r1=~AWin_v_Neut_L_NAc_r1       19         5 -0.014
## 96            Appr_NAcc_r1=~AWin_v_Neut_R_NAc_r1       20         1 -0.023
## 97            Appr_NAcc_r1=~AWin_v_Neut_R_NAc_r1       20         2 -0.012
## 98            Appr_NAcc_r1=~AWin_v_Neut_R_NAc_r1       20         3  0.016
## 99            Appr_NAcc_r1=~AWin_v_Neut_R_NAc_r1       20         4  0.002
## 100           Appr_NAcc_r1=~AWin_v_Neut_R_NAc_r1       20         5 -0.018
## 101           Appr_NAcc_r1=~BWin_v_Neut_L_NAc_r1       21         1 -0.040
## 102           Appr_NAcc_r1=~BWin_v_Neut_L_NAc_r1       21         2 -0.018
## 103           Appr_NAcc_r1=~BWin_v_Neut_L_NAc_r1       21         3  0.019
## 104           Appr_NAcc_r1=~BWin_v_Neut_L_NAc_r1       21         4  0.014
## 105           Appr_NAcc_r1=~BWin_v_Neut_L_NAc_r1       21         5 -0.019
## 106           Appr_NAcc_r1=~BWin_v_Neut_R_NAc_r1       22         1 -0.010
## 107           Appr_NAcc_r1=~BWin_v_Neut_R_NAc_r1       22         2 -0.014
## 108           Appr_NAcc_r1=~BWin_v_Neut_R_NAc_r1       22         3  0.010
## 109           Appr_NAcc_r1=~BWin_v_Neut_R_NAc_r1       22         4  0.007
## 110           Appr_NAcc_r1=~BWin_v_Neut_R_NAc_r1       22         5 -0.002
## 111          Appr_NAcc_r1=~BWin_v_BLose_L_NAc_r1       23         1  0.007
## 112          Appr_NAcc_r1=~BWin_v_BLose_L_NAc_r1       23         2  0.017
## 113          Appr_NAcc_r1=~BWin_v_BLose_L_NAc_r1       23         3  0.003
## 114          Appr_NAcc_r1=~BWin_v_BLose_L_NAc_r1       23         4 -0.025
## 115          Appr_NAcc_r1=~BWin_v_BLose_L_NAc_r1       23         5 -0.061
## 116          Appr_NAcc_r1=~BWin_v_BLose_R_NAc_r1       24         1  0.044
## 117          Appr_NAcc_r1=~BWin_v_BLose_R_NAc_r1       24         2  0.032
## 118          Appr_NAcc_r1=~BWin_v_BLose_R_NAc_r1       24         3 -0.010
## 119          Appr_NAcc_r1=~BWin_v_BLose_R_NAc_r1       24         4 -0.041
## 120          Appr_NAcc_r1=~BWin_v_BLose_R_NAc_r1       24         5 -0.069
## 121   AWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       25         1  0.006
## 122   AWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       25         2  0.006
## 123   AWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       25         3 -0.004
## 124   AWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       25         4 -0.004
## 125   AWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       25         5 -0.005
## 126   AWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       26         1  0.000
## 127   AWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       26         2  0.000
## 128   AWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       26         3  0.003
## 129   AWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       26         4 -0.002
## 130   AWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       26         5 -0.025
## 131   AWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       27         1  0.001
## 132   AWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       27         2  0.004
## 133   AWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       27         3 -0.002
## 134   AWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       27         4 -0.002
## 135   AWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       27         5 -0.001
## 136   AWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       28         1 -0.004
## 137   AWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       28         2 -0.001
## 138   AWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       28         3  0.005
## 139   AWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       28         4 -0.004
## 140   AWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       28         5 -0.006
## 141   AWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       29         1  0.000
## 142   AWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       29         2 -0.001
## 143   AWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       29         3  0.002
## 144   AWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       29         4 -0.001
## 145   AWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       29         5 -0.004
## 146   AWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       30         1  0.001
## 147   AWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       30         2  0.000
## 148   AWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       30         3  0.000
## 149   AWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       30         4 -0.001
## 150   AWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       30         5 -0.003
## 151   AWin_v_Neut_R_Ins_r2~~AWin_v_Neut_R_Ins_r2       31         1  0.000
## 152   AWin_v_Neut_R_Ins_r2~~AWin_v_Neut_R_Ins_r2       31         2  0.001
## 153   AWin_v_Neut_R_Ins_r2~~AWin_v_Neut_R_Ins_r2       31         3  0.000
## 154   AWin_v_Neut_R_Ins_r2~~AWin_v_Neut_R_Ins_r2       31         4  0.000
## 155   AWin_v_Neut_R_Ins_r2~~AWin_v_Neut_R_Ins_r2       31         5  0.000
## 156   BWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       32         1  0.001
## 157   BWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       32         2 -0.002
## 158   BWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       32         3  0.002
## 159   BWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       32         4  0.000
## 160   BWin_v_Neut_R_Ins_r2~~BWin_v_Neut_R_Ins_r2       32         5 -0.007
## 161 ALose_v_Neut_L_Ins_r2~~ALose_v_Neut_L_Ins_r2       33         1  0.003
## 162 ALose_v_Neut_L_Ins_r2~~ALose_v_Neut_L_Ins_r2       33         2  0.000
## 163 ALose_v_Neut_L_Ins_r2~~ALose_v_Neut_L_Ins_r2       33         3  0.000
## 164 ALose_v_Neut_L_Ins_r2~~ALose_v_Neut_L_Ins_r2       33         4 -0.002
## 165 ALose_v_Neut_L_Ins_r2~~ALose_v_Neut_L_Ins_r2       33         5 -0.004
## 166 ALose_v_Neut_R_Ins_r2~~ALose_v_Neut_R_Ins_r2       34         1  0.000
## 167 ALose_v_Neut_R_Ins_r2~~ALose_v_Neut_R_Ins_r2       34         2  0.000
## 168 ALose_v_Neut_R_Ins_r2~~ALose_v_Neut_R_Ins_r2       34         3  0.000
## 169 ALose_v_Neut_R_Ins_r2~~ALose_v_Neut_R_Ins_r2       34         4  0.000
## 170 ALose_v_Neut_R_Ins_r2~~ALose_v_Neut_R_Ins_r2       34         5 -0.001
## 171 BLose_v_Neut_L_Ins_r2~~BLose_v_Neut_L_Ins_r2       35         1  0.004
## 172 BLose_v_Neut_L_Ins_r2~~BLose_v_Neut_L_Ins_r2       35         2  0.000
## 173 BLose_v_Neut_L_Ins_r2~~BLose_v_Neut_L_Ins_r2       35         3  0.002
## 174 BLose_v_Neut_L_Ins_r2~~BLose_v_Neut_L_Ins_r2       35         4 -0.005
## 175 BLose_v_Neut_L_Ins_r2~~BLose_v_Neut_L_Ins_r2       35         5 -0.007
## 176 BLose_v_Neut_R_Ins_r2~~BLose_v_Neut_R_Ins_r2       36         1  0.000
## 177 BLose_v_Neut_R_Ins_r2~~BLose_v_Neut_R_Ins_r2       36         2  0.000
## 178 BLose_v_Neut_R_Ins_r2~~BLose_v_Neut_R_Ins_r2       36         3  0.001
## 179 BLose_v_Neut_R_Ins_r2~~BLose_v_Neut_R_Ins_r2       36         4 -0.001
## 180 BLose_v_Neut_R_Ins_r2~~BLose_v_Neut_R_Ins_r2       36         5 -0.001
## 181   AWin_v_Neut_L_NAc_r2~~AWin_v_Neut_L_NAc_r2       37         1  0.001
## 182   AWin_v_Neut_L_NAc_r2~~AWin_v_Neut_L_NAc_r2       37         2 -0.002
## 183   AWin_v_Neut_L_NAc_r2~~AWin_v_Neut_L_NAc_r2       37         3  0.003
## 184   AWin_v_Neut_L_NAc_r2~~AWin_v_Neut_L_NAc_r2       37         4 -0.001
## 185   AWin_v_Neut_L_NAc_r2~~AWin_v_Neut_L_NAc_r2       37         5 -0.021
## 186   AWin_v_Neut_R_NAc_r2~~AWin_v_Neut_R_NAc_r2       38         1 -0.003
## 187   AWin_v_Neut_R_NAc_r2~~AWin_v_Neut_R_NAc_r2       38         2 -0.001
## 188   AWin_v_Neut_R_NAc_r2~~AWin_v_Neut_R_NAc_r2       38         3  0.004
## 189   AWin_v_Neut_R_NAc_r2~~AWin_v_Neut_R_NAc_r2       38         4 -0.003
## 190   AWin_v_Neut_R_NAc_r2~~AWin_v_Neut_R_NAc_r2       38         5 -0.006
## 191   BWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       39         1  0.001
## 192   BWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       39         2  0.004
## 193   BWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       39         3  0.002
## 194   BWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       39         4 -0.005
## 195   BWin_v_Neut_L_NAc_r2~~BWin_v_Neut_L_NAc_r2       39         5 -0.031
## 196   BWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       40         1 -0.006
## 197   BWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       40         2 -0.001
## 198   BWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       40         3  0.005
## 199   BWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       40         4 -0.004
## 200   BWin_v_Neut_R_NAc_r2~~BWin_v_Neut_R_NAc_r2       40         5 -0.004
## 201 BWin_v_BLose_L_NAc_r2~~BWin_v_BLose_L_NAc_r2       41         1  0.000
## 202 BWin_v_BLose_L_NAc_r2~~BWin_v_BLose_L_NAc_r2       41         2  0.006
## 203 BWin_v_BLose_L_NAc_r2~~BWin_v_BLose_L_NAc_r2       41         3 -0.001
## 204 BWin_v_BLose_L_NAc_r2~~BWin_v_BLose_L_NAc_r2       41         4 -0.005
## 205 BWin_v_BLose_L_NAc_r2~~BWin_v_BLose_L_NAc_r2       41         5 -0.006
## 206 BWin_v_BLose_R_NAc_r2~~BWin_v_BLose_R_NAc_r2       42         1  0.005
## 207 BWin_v_BLose_R_NAc_r2~~BWin_v_BLose_R_NAc_r2       42         2 -0.002
## 208 BWin_v_BLose_R_NAc_r2~~BWin_v_BLose_R_NAc_r2       42         3 -0.003
## 209 BWin_v_BLose_R_NAc_r2~~BWin_v_BLose_R_NAc_r2       42         4  0.005
## 210 BWin_v_BLose_R_NAc_r2~~BWin_v_BLose_R_NAc_r2       42         5  0.011
## 211   AWin_v_Neut_R_Ins_r1~~AWin_v_Neut_R_Ins_r1       43         1 -0.001
## 212   AWin_v_Neut_R_Ins_r1~~AWin_v_Neut_R_Ins_r1       43         2 -0.001
## 213   AWin_v_Neut_R_Ins_r1~~AWin_v_Neut_R_Ins_r1       43         3  0.002
## 214   AWin_v_Neut_R_Ins_r1~~AWin_v_Neut_R_Ins_r1       43         4 -0.002
## 215   AWin_v_Neut_R_Ins_r1~~AWin_v_Neut_R_Ins_r1       43         5 -0.003
## 216   BWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       44         1  0.004
## 217   BWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       44         2 -0.001
## 218   BWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       44         3  0.001
## 219   BWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       44         4 -0.002
## 220   BWin_v_Neut_R_Ins_r1~~BWin_v_Neut_R_Ins_r1       44         5 -0.006
## 221 ALose_v_Neut_L_Ins_r1~~ALose_v_Neut_L_Ins_r1       45         1 -0.002
## 222 ALose_v_Neut_L_Ins_r1~~ALose_v_Neut_L_Ins_r1       45         2  0.000
## 223 ALose_v_Neut_L_Ins_r1~~ALose_v_Neut_L_Ins_r1       45         3  0.001
## 224 ALose_v_Neut_L_Ins_r1~~ALose_v_Neut_L_Ins_r1       45         4  0.000
## 225 ALose_v_Neut_L_Ins_r1~~ALose_v_Neut_L_Ins_r1       45         5 -0.001
## 226 ALose_v_Neut_R_Ins_r1~~ALose_v_Neut_R_Ins_r1       46         1  0.001
## 227 ALose_v_Neut_R_Ins_r1~~ALose_v_Neut_R_Ins_r1       46         2  0.000
## 228 ALose_v_Neut_R_Ins_r1~~ALose_v_Neut_R_Ins_r1       46         3  0.000
## 229 ALose_v_Neut_R_Ins_r1~~ALose_v_Neut_R_Ins_r1       46         4 -0.001
## 230 ALose_v_Neut_R_Ins_r1~~ALose_v_Neut_R_Ins_r1       46         5 -0.001
## 231 BLose_v_Neut_L_Ins_r1~~BLose_v_Neut_L_Ins_r1       47         1  0.003
## 232 BLose_v_Neut_L_Ins_r1~~BLose_v_Neut_L_Ins_r1       47         2  0.002
## 233 BLose_v_Neut_L_Ins_r1~~BLose_v_Neut_L_Ins_r1       47         3  0.000
## 234 BLose_v_Neut_L_Ins_r1~~BLose_v_Neut_L_Ins_r1       47         4 -0.003
## 235 BLose_v_Neut_L_Ins_r1~~BLose_v_Neut_L_Ins_r1       47         5 -0.003
## 236 BLose_v_Neut_R_Ins_r1~~BLose_v_Neut_R_Ins_r1       48         1 -0.001
## 237 BLose_v_Neut_R_Ins_r1~~BLose_v_Neut_R_Ins_r1       48         2  0.000
## 238 BLose_v_Neut_R_Ins_r1~~BLose_v_Neut_R_Ins_r1       48         3  0.001
## 239 BLose_v_Neut_R_Ins_r1~~BLose_v_Neut_R_Ins_r1       48         4 -0.001
## 240 BLose_v_Neut_R_Ins_r1~~BLose_v_Neut_R_Ins_r1       48         5 -0.002
## 241   AWin_v_Neut_L_NAc_r1~~AWin_v_Neut_L_NAc_r1       49         1  0.003
## 242   AWin_v_Neut_L_NAc_r1~~AWin_v_Neut_L_NAc_r1       49         2  0.004
## 243   AWin_v_Neut_L_NAc_r1~~AWin_v_Neut_L_NAc_r1       49         3 -0.002
## 244   AWin_v_Neut_L_NAc_r1~~AWin_v_Neut_L_NAc_r1       49         4 -0.002
## 245   AWin_v_Neut_L_NAc_r1~~AWin_v_Neut_L_NAc_r1       49         5 -0.003
## 246   AWin_v_Neut_R_NAc_r1~~AWin_v_Neut_R_NAc_r1       50         1 -0.001
## 247   AWin_v_Neut_R_NAc_r1~~AWin_v_Neut_R_NAc_r1       50         2  0.003
## 248   AWin_v_Neut_R_NAc_r1~~AWin_v_Neut_R_NAc_r1       50         3 -0.002
## 249   AWin_v_Neut_R_NAc_r1~~AWin_v_Neut_R_NAc_r1       50         4  0.000
## 250   AWin_v_Neut_R_NAc_r1~~AWin_v_Neut_R_NAc_r1       50         5  0.002
## 251   BWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       51         1  0.007
## 252   BWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       51         2  0.009
## 253   BWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       51         3 -0.005
## 254   BWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       51         4 -0.006
## 255   BWin_v_Neut_L_NAc_r1~~BWin_v_Neut_L_NAc_r1       51         5 -0.008
## 256   BWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       52         1  0.000
## 257   BWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       52         2  0.005
## 258   BWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       52         3 -0.001
## 259   BWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       52         4 -0.003
## 260   BWin_v_Neut_R_NAc_r1~~BWin_v_Neut_R_NAc_r1       52         5 -0.005
## 261 BWin_v_BLose_L_NAc_r1~~BWin_v_BLose_L_NAc_r1       53         1  0.000
## 262 BWin_v_BLose_L_NAc_r1~~BWin_v_BLose_L_NAc_r1       53         2 -0.001
## 263 BWin_v_BLose_L_NAc_r1~~BWin_v_BLose_L_NAc_r1       53         3  0.002
## 264 BWin_v_BLose_L_NAc_r1~~BWin_v_BLose_L_NAc_r1       53         4 -0.001
## 265 BWin_v_BLose_L_NAc_r1~~BWin_v_BLose_L_NAc_r1       53         5 -0.003
## 266 BWin_v_BLose_R_NAc_r1~~BWin_v_BLose_R_NAc_r1       54         1  0.020
## 267 BWin_v_BLose_R_NAc_r1~~BWin_v_BLose_R_NAc_r1       54         2  0.001
## 268 BWin_v_BLose_R_NAc_r1~~BWin_v_BLose_R_NAc_r1       54         3 -0.001
## 269 BWin_v_BLose_R_NAc_r1~~BWin_v_BLose_R_NAc_r1       54         4 -0.008
## 270 BWin_v_BLose_R_NAc_r1~~BWin_v_BLose_R_NAc_r1       54         5 -0.016
## 271             Avoid_Insula_r2~~Avoid_Insula_r2       55         1  0.000
## 272             Avoid_Insula_r2~~Avoid_Insula_r2       55         2  0.000
## 273             Avoid_Insula_r2~~Avoid_Insula_r2       55         3  0.000
## 274             Avoid_Insula_r2~~Avoid_Insula_r2       55         4  0.000
## 275             Avoid_Insula_r2~~Avoid_Insula_r2       55         5  0.000
## 276                   Appr_NAcc_r2~~Appr_NAcc_r2       56         1  0.000
## 277                   Appr_NAcc_r2~~Appr_NAcc_r2       56         2  0.000
## 278                   Appr_NAcc_r2~~Appr_NAcc_r2       56         3  0.000
## 279                   Appr_NAcc_r2~~Appr_NAcc_r2       56         4  0.000
## 280                   Appr_NAcc_r2~~Appr_NAcc_r2       56         5  0.000
## 281             Avoid_Insula_r1~~Avoid_Insula_r1       57         1  0.000
## 282             Avoid_Insula_r1~~Avoid_Insula_r1       57         2  0.000
## 283             Avoid_Insula_r1~~Avoid_Insula_r1       57         3  0.000
## 284             Avoid_Insula_r1~~Avoid_Insula_r1       57         4  0.000
## 285             Avoid_Insula_r1~~Avoid_Insula_r1       57         5  0.000
## 286                   Appr_NAcc_r1~~Appr_NAcc_r1       58         1  0.000
## 287                   Appr_NAcc_r1~~Appr_NAcc_r1       58         2  0.000
## 288                   Appr_NAcc_r1~~Appr_NAcc_r1       58         3  0.000
## 289                   Appr_NAcc_r1~~Appr_NAcc_r1       58         4  0.000
## 290                   Appr_NAcc_r1~~Appr_NAcc_r1       58         5  0.000
## 291                Avoid_Insula_r2~~Appr_NAcc_r2       59         1  0.157
## 292                Avoid_Insula_r2~~Appr_NAcc_r2       59         2 -0.096
## 293                Avoid_Insula_r2~~Appr_NAcc_r2       59         3 -0.048
## 294                Avoid_Insula_r2~~Appr_NAcc_r2       59         4  0.092
## 295                Avoid_Insula_r2~~Appr_NAcc_r2       59         5  0.296
## 296             Avoid_Insula_r2~~Avoid_Insula_r1       60         1 -0.034
## 297             Avoid_Insula_r2~~Avoid_Insula_r1       60         2 -0.030
## 298             Avoid_Insula_r2~~Avoid_Insula_r1       60         3  0.067
## 299             Avoid_Insula_r2~~Avoid_Insula_r1       60         4 -0.052
## 300             Avoid_Insula_r2~~Avoid_Insula_r1       60         5 -0.051
## 301                Avoid_Insula_r2~~Appr_NAcc_r1       61         1  0.185
## 302                Avoid_Insula_r2~~Appr_NAcc_r1       61         2  0.042
## 303                Avoid_Insula_r2~~Appr_NAcc_r1       61         3 -0.046
## 304                Avoid_Insula_r2~~Appr_NAcc_r1       61         4 -0.063
## 305                Avoid_Insula_r2~~Appr_NAcc_r1       61         5 -0.099
## 306                Appr_NAcc_r2~~Avoid_Insula_r1       62         1  0.012
## 307                Appr_NAcc_r2~~Avoid_Insula_r1       62         2  0.086
## 308                Appr_NAcc_r2~~Avoid_Insula_r1       62         3 -0.036
## 309                Appr_NAcc_r2~~Avoid_Insula_r1       62         4 -0.057
## 310                Appr_NAcc_r2~~Avoid_Insula_r1       62         5  0.004
## 311                   Appr_NAcc_r2~~Appr_NAcc_r1       63         1  0.026
## 312                   Appr_NAcc_r2~~Appr_NAcc_r1       63         2 -0.059
## 313                   Appr_NAcc_r2~~Appr_NAcc_r1       63         3  0.003
## 314                   Appr_NAcc_r2~~Appr_NAcc_r1       63         4  0.058
## 315                   Appr_NAcc_r2~~Appr_NAcc_r1       63         5  0.007
## 316                Avoid_Insula_r1~~Appr_NAcc_r1       64         1  0.001
## 317                Avoid_Insula_r1~~Appr_NAcc_r1       64         2 -0.107
## 318                Avoid_Insula_r1~~Appr_NAcc_r1       64         3  0.035
## 319                Avoid_Insula_r1~~Appr_NAcc_r1       64         4  0.063
## 320                Avoid_Insula_r1~~Appr_NAcc_r1       64         5  0.148
## 321                                        rmsea       65         1  0.004
## 322                                        rmsea       65         2  0.004
## 323                                        rmsea       65         3  0.006
## 324                                        rmsea       65         4 -0.007
## 325                                        rmsea       65         5 -0.085
## 326                                          cfi       66         1 -0.009
## 327                                          cfi       66         2 -0.008
## 328                                          cfi       66         3 -0.011
## 329                                          cfi       66         4  0.016
## 330                                          cfi       66         5  0.168
## 331                                          tli       67         1 -0.011
## 332                                          tli       67         2 -0.009
## 333                                          tli       67         3 -0.013
## 334                                          tli       67         4  0.018
## 335                                          tli       67         5  0.193
## 336                                          gfi       68         1 -0.068
## 337                                          gfi       68         2  0.009
## 338                                          gfi       68         3  0.013
## 339                                          gfi       68         4  0.009
## 340                                          gfi       68         5 -0.070
## 341                                         srmr       69         1  0.027
## 342                                         srmr       69         2  0.001
## 343                                         srmr       69         3 -0.005
## 344                                         srmr       69         4 -0.007
## 345                                         srmr       69         5  0.007
##         p
## 1   0.092
## 2   0.456
## 3   0.412
## 4   0.228
## 5   0.730
## 6   0.048
## 7   0.452
## 8   0.332
## 9   0.202
## 10  0.750
## 11  0.032
## 12  0.130
## 13  0.154
## 14  0.110
## 15  0.032
## 16  0.122
## 17  0.038
## 18  0.714
## 19  0.006
## 20  0.044
## 21  0.204
## 22  0.374
## 23  0.774
## 24  0.250
## 25  0.058
## 26  0.484
## 27  0.082
## 28  0.658
## 29  0.008
## 30  0.058
## 31  0.578
## 32  0.242
## 33  0.748
## 34  0.152
## 35  0.066
## 36  0.812
## 37  0.780
## 38  0.720
## 39  0.782
## 40  0.458
## 41  0.750
## 42  0.284
## 43  0.636
## 44  0.158
## 45  0.092
## 46  0.992
## 47  0.720
## 48  0.690
## 49  0.962
## 50  0.796
## 51  0.848
## 52  0.436
## 53  0.772
## 54  0.384
## 55  0.118
## 56  0.736
## 57  0.268
## 58  0.156
## 59  0.078
## 60  0.036
## 61  0.840
## 62  0.914
## 63  0.590
## 64  0.860
## 65  0.646
## 66  0.464
## 67  0.508
## 68  0.694
## 69  0.462
## 70  0.704
## 71  0.696
## 72  0.264
## 73  0.840
## 74  0.260
## 75  0.990
## 76  0.098
## 77  0.880
## 78  0.272
## 79  0.830
## 80  0.296
## 81  0.310
## 82  0.678
## 83  0.548
## 84  0.622
## 85  0.406
## 86  0.134
## 87  0.196
## 88  0.154
## 89  0.200
## 90  0.112
## 91  0.328
## 92  0.502
## 93  0.316
## 94  0.666
## 95  0.790
## 96  0.522
## 97  0.510
## 98  0.280
## 99  0.926
## 100 0.742
## 101 0.324
## 102 0.414
## 103 0.306
## 104 0.610
## 105 0.754
## 106 0.764
## 107 0.404
## 108 0.580
## 109 0.764
## 110 1.000
## 111 0.778
## 112 0.332
## 113 0.790
## 114 0.248
## 115 0.108
## 116 0.242
## 117 0.156
## 118 0.584
## 119 0.142
## 120 0.152
## 121 0.550
## 122 0.306
## 123 0.342
## 124 0.644
## 125 0.758
## 126 0.920
## 127 0.988
## 128 0.416
## 129 0.750
## 130 0.032
## 131 0.888
## 132 0.378
## 133 0.566
## 134 0.770
## 135 0.996
## 136 0.730
## 137 0.728
## 138 0.206
## 139 0.590
## 140 0.644
## 141 0.906
## 142 0.386
## 143 0.096
## 144 0.520
## 145 0.356
## 146 0.774
## 147 0.864
## 148 0.986
## 149 0.896
## 150 0.722
## 151 0.974
## 152 0.674
## 153 0.900
## 154 0.956
## 155 0.800
## 156 0.780
## 157 0.662
## 158 0.610
## 159 1.000
## 160 0.396
## 161 0.370
## 162 0.904
## 163 0.698
## 164 0.338
## 165 0.346
## 166 0.780
## 167 0.850
## 168 0.770
## 169 0.998
## 170 0.548
## 171 0.278
## 172 0.888
## 173 0.328
## 174 0.092
## 175 0.182
## 176 0.956
## 177 0.840
## 178 0.240
## 179 0.548
## 180 0.672
## 181 0.738
## 182 0.664
## 183 0.478
## 184 0.988
## 185 0.044
## 186 0.874
## 187 0.688
## 188 0.308
## 189 0.694
## 190 0.640
## 191 0.850
## 192 0.454
## 193 0.624
## 194 0.444
## 195 0.012
## 196 0.664
## 197 0.856
## 198 0.244
## 199 0.554
## 200 0.842
## 201 0.916
## 202 0.172
## 203 0.842
## 204 0.284
## 205 0.578
## 206 0.406
## 207 0.676
## 208 0.196
## 209 0.358
## 210 0.204
## 211 0.740
## 212 0.672
## 213 0.078
## 214 0.332
## 215 0.414
## 216 0.304
## 217 0.570
## 218 0.500
## 219 0.556
## 220 0.388
## 221 0.594
## 222 0.894
## 223 0.582
## 224 0.848
## 225 0.970
## 226 0.390
## 227 0.546
## 228 0.938
## 229 0.394
## 230 0.482
## 231 0.416
## 232 0.294
## 233 0.766
## 234 0.188
## 235 0.650
## 236 0.520
## 237 0.792
## 238 0.252
## 239 0.530
## 240 0.466
## 241 0.660
## 242 0.484
## 243 0.516
## 244 0.746
## 245 0.876
## 246 0.994
## 247 0.504
## 248 0.500
## 249 0.876
## 250 0.674
## 251 0.502
## 252 0.192
## 253 0.308
## 254 0.500
## 255 0.630
## 256 0.934
## 257 0.320
## 258 0.762
## 259 0.590
## 260 0.706
## 261 0.970
## 262 0.764
## 263 0.668
## 264 0.762
## 265 0.870
## 266 0.120
## 267 0.780
## 268 0.790
## 269 0.328
## 270 0.258
## 271 1.000
## 272 1.000
## 273 1.000
## 274 1.000
## 275 1.000
## 276 1.000
## 277 1.000
## 278 1.000
## 279 1.000
## 280 1.000
## 281 1.000
## 282 1.000
## 283 1.000
## 284 1.000
## 285 1.000
## 286 1.000
## 287 1.000
## 288 1.000
## 289 1.000
## 290 1.000
## 291 0.260
## 292 0.176
## 293 0.398
## 294 0.314
## 295 0.070
## 296 0.704
## 297 0.642
## 298 0.144
## 299 0.522
## 300 0.706
## 301 0.110
## 302 0.490
## 303 0.330
## 304 0.416
## 305 0.540
## 306 0.892
## 307 0.170
## 308 0.430
## 309 0.476
## 310 0.992
## 311 0.844
## 312 0.482
## 313 0.972
## 314 0.582
## 315 0.990
## 316 0.998
## 317 0.240
## 318 0.666
## 319 0.632
## 320 0.496
## 321 0.060
## 322 0.050
## 323 0.000
## 324 0.016
## 325 0.000
## 326 0.136
## 327 0.116
## 328 0.002
## 329 0.080
## 330 0.000
## 331 0.136
## 332 0.116
## 333 0.002
## 334 0.080
## 335 0.000
## 336 0.104
## 337 0.812
## 338 0.802
## 339 0.256
## 340 0.786
## 341 0.268
## 342 0.780
## 343 0.850
## 344 0.446
## 345 0.532

8.5 Plot LSEM

Plotting the lsem.estimate sig for selected indices, parents

plot(lsem.MID_par, parindex=c(3,4,6, # not significant
                              12, # significant
                              63:69))

Plotting the lsem.estimate sig for selected indices, youth

plot(lsem.MID_yth, parindex=c(3,4,6, #significant
                              12, # not significant
                              63:69))

9 Sensitivity Analyses

In the manuscript, several sensitivity analyses are proposed:

1. Differences (CFA/EFA) in effects across data collected only at UM site.
2. Resampling of CFA/EFA in effects across larger ABCD data to evaluate the stability of model effects
3. Invariance across sex at birth

9.1 UM Specific CFA/ESEM/EFA

UM Only data

um_only = rbind(ahrb_df,mls_df)

9.1.1 CFA

um_allsample <- cfa(model = mid_model, data = um_only,
                     estimator = "ML", std.lv = FALSE, meanstructure = TRUE)

um_config_cfa <- cfa(model = mid_model, data = um_only, group = 'set',
                     estimator = "ML", std.lv = FALSE, meanstructure = TRUE)

um_metric_cfa <-cfa(model = mid_model, data = um_only,
                    group = 'set', group.equal=c("loadings"),
                    estimator = "ML", std.lv = FALSE, meanstructure = TRUE)

umsite_out <- matrix(NA, ncol = 10, nrow = 3)
colnames(umsite_out) <- c("model","chisq","df","pvalue", "rmsea", "cfi", "srmr", "tli",
                   "AIC", "BIC")

# save fit measures from models
umsite_out[1,2:8] <- round(data.matrix(fitmeasures(um_allsample, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi", "srmr", "tli"))), 
                    digits=3)

umsite_out[2,2:8] <- round(data.matrix(fitmeasures(um_config_cfa, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi", "srmr","tli"))), 
                            digits=3)

umsite_out[3,2:8] <- round(data.matrix(fitmeasures(um_metric_cfa, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi", "srmr","tli"))), 
                    digits=3)

umsite_out[1,9] <- round(AIC(um_allsample),3)
umsite_out[2,9] <- round(AIC(um_config_cfa),3)
umsite_out[3,9] <- round(AIC(um_metric_cfa),3)

# BIC models
umsite_out[1,10] <- round(BIC(um_allsample),3)
umsite_out[2,10] <- round(BIC(um_config_cfa),3)
umsite_out[3,10] <- round(BIC(um_metric_cfa),3)

umsite_out[1:3,1] <-  c("Overall CFA", "Config MG-CFA", "Metric MG-CFA")

umsite_out %>% 
  knitr::kable(
    caption = "Fit statistics from MG-CFA and ESEM models",
    booktabs = TRUE,align = 'c'
    )

Fit statistics from MG-CFA and ESEM models

model	chisq	df	pvalue	rmsea	cfi	srmr	tli	AIC	BIC
Overall CFA	8843.46	354	0	0.339	0.132	0.197	0.073	-3855.033	-3587.646
Config MG-CFA	9229.864	713	0	0.338	0.133	0.206	0.081	-3953.772	-3435.711
Metric MG-CFA	9343.756	729	0	0.336	0.123	0.208	0.091	-3871.881	-3407.297

9.1.2 EFA

In this case, only the data for the ABCD sample changes (reduced from 21 –> 1 site [UM]). Hence, rerunning only the ABCD EFA. Factor congruence estimation will use EFA from above for AHRB and MLS.

Did not run UM only ABCD sample. GE data not available, hence no site-13

fa_cong_um = fa.congruence(x = list(ahrb_efa,mls_efa), digits = 2) 

# rename rows/columns to improve interpretability

colnames(fa_cong_um) <- c(ahrb_colnames,mls_colnames)
rownames(fa_cong_um) <- c(ahrb_colnames,mls_colnames)
fa_cong_um %>% 
  knitr::kable(
    caption = "Factor Congruence: AHRB & MLS EFA",
    booktabs = TRUE
    )

Factor Congruence: AHRB & MLS EFA

	AB1	AB2	AB3	AB4	AB5	AB6	MS1	MS2	MS3	MS4	MS5	MS6	MS7
AB1	1.00	-0.01	0.03	0.03	0.03	0.02	0.05	0.01	0.90	0.00	0.04	0.45	0.11
AB2	-0.01	1.00	0.03	-0.03	0.08	0.01	-0.02	0.04	0.00	0.91	-0.24	-0.02	-0.04
AB3	0.03	0.03	1.00	0.00	0.03	0.03	0.85	0.01	0.00	0.01	-0.02	-0.04	0.08
AB4	0.03	-0.03	0.00	1.00	0.09	-0.07	0.04	0.97	0.05	-0.01	0.13	-0.08	-0.07
AB5	0.03	0.08	0.03	0.09	1.00	0.05	0.00	-0.01	0.02	0.31	0.89	-0.09	0.03
AB6	0.02	0.01	0.03	-0.07	0.05	1.00	0.00	0.03	-0.28	0.02	0.06	0.26	0.89
MS1	0.05	-0.02	0.85	0.04	0.00	0.00	1.00	0.06	-0.04	0.01	0.03	0.08	-0.01
MS2	0.01	0.04	0.01	0.97	-0.01	0.03	0.06	1.00	0.03	0.04	0.05	-0.07	0.01
MS3	0.90	0.00	0.00	0.05	0.02	-0.28	-0.04	0.03	1.00	-0.02	0.00	0.08	-0.08
MS4	0.00	0.91	0.01	-0.01	0.31	0.02	0.01	0.04	-0.02	1.00	0.05	0.01	-0.01
MS5	0.04	-0.24	-0.02	0.13	0.89	0.06	0.03	0.05	0.00	0.05	1.00	-0.02	0.02
MS6	0.45	-0.02	-0.04	-0.08	-0.09	0.26	0.08	-0.07	0.08	0.01	-0.02	1.00	-0.03
MS7	0.11	-0.04	0.08	-0.07	0.03	0.89	-0.01	0.01	-0.08	-0.01	0.02	-0.03	1.00

corrplot(fa_cong_um, method = "color", tl.cex = .8, type = "lower")

9.2 Resampling ABCD CFA/EFA

For resampling of the CFA model, using bootstrapLavaan for lavaan. First fitting the cfa model, then creating 1000 bootstrapped sampled and extracting fit statistics

set.seed(1111)
boot_cfa <- cfa(model = mid_model, data = abcd_df2,
                 estimator = "ML", std.lv = FALSE, meanstructure = TRUE)

out_cfaboot <- bootstrapLavaan(object = boot_cfa, R = 1000, 
                               FUN = fitMeasures,
                               fit.measures=c("chisq","rmsea","cfi",
                                              "tli","srmr","AIC","BIC"),
                               parallel="multicore", ncpus=4)

cfaboot_df <- data.frame(out_cfaboot)

For the resampling of the EFA model, using sample_n to get [300] samples of N = 300 (w/ replacement) of ABCD data. Then, estimating recommended N of factors per paralell analysis. Saving this to dataframe

# create empty df where data will be saved and compiled for models
#resampled_cfa <- matrix(NA, ncol = 11, nrow = 50) # resampling 50x for Config + #Metric models
#colnames(resampled_cfa) <- c("Sample",
#                              "chisq","df","pvalue", 
#                              "rmsea","cfi","tli","srmr","AIC","BIC","Factors")
#
#n_loop = 50

sample_size = 300

resampled_cfa <- matrix(NA, ncol = 2, nrow = sample_size) # resampling 50x for Config + Metric models
colnames(resampled_cfa) <- c("Sample","Factors")

  
for (s in 1:sample_size) {
  
  sub_df <- sample_n(tbl = abcd_df2[,mod_vars], size = sample_size, replace = TRUE)
  
  resampled_cfa[s,1] <- s

  val <- nScree(x=sub_df[,mod_vars],model="factors")
  resampled_cfa[s,2] <- as.integer(val$Components[3])
  

}

resampled_res <- data.frame(resampled_cfa)

Plotting the mean + 95% Confidence interval of values

n = nrow(out_cfaboot)

ci_plt1 <- cfaboot_df %>% 
  gather(key = "FitIndex", value = "Statistic",
         srmr,rmsea) %>% 
  dplyr::group_by(FitIndex) %>% 
  dplyr::summarize(m = mean(Statistic), stdev = sd(Statistic)) %>% 
  ggplot(aes(x =FitIndex, y = m, fill = FitIndex, color=FitIndex)) +
  geom_point()+
  geom_errorbar(aes(ymin=m-(1.96*stdev/sqrt(n)),
                    ymax=m+(1.96*stdev/sqrt(n))), 
                width=.2,
                position=position_dodge(0.05))+
  labs(
    title = 'CFA: RMSEA & SRMR',
    x = 'Fit Stats',
    y = 'Type',
  )+
  theme_minimal()


ci_plt2 <- cfaboot_df %>% 
  gather(key = "FitIndex", value = "Statistic",
         cfi,tli) %>% 
  dplyr::group_by(FitIndex) %>% 
  dplyr::summarize(m = mean(Statistic), stdev = sd(Statistic)) %>% 
  ggplot(aes(x =FitIndex, y = m, fill = FitIndex, color=FitIndex)) +
  geom_point()+
  geom_errorbar(aes(ymin=m-(1.96*stdev/sqrt(n)),
                    ymax=m+(1.96*stdev/sqrt(n))), 
                width=.2,
                position=position_dodge(0.05))+
  labs(
    title = 'CFA: CFI & TLI',
    x = 'Fit Stats',
    y = 'Type',
  )+
  theme_minimal()


ci_plt3 <- cfaboot_df %>% 
  gather(key = "FitIndex", value = "Statistic",
         aic,bic) %>% 
  dplyr::group_by(FitIndex) %>% 
  dplyr::summarize(m = mean(Statistic), stdev = sd(Statistic)) %>% 
  ggplot(aes(x =FitIndex, y = m, fill = FitIndex, color=FitIndex)) +
  geom_point()+
  geom_errorbar(aes(ymin=m-(1.96*stdev/sqrt(n)),
                    ymax=m+(1.96*stdev/sqrt(n))), 
                width=.2,
                position=position_dodge(0.05))+
  labs(
    title = 'CFA: AIC & BIC',
    x = 'Fit Stats',
    y = 'Type',
  )+
  theme_minimal()


ci_plt4 = resampled_res %>%
  dplyr::summarize(m = mean(Factors), stdev = sd(Factors)) %>% 
  ggplot(aes(x ="", y = m)) +
  geom_point()+
  geom_errorbar(aes(ymin=m-(1.96*stdev/sqrt(n)),
                    ymax=m+(1.96*stdev/sqrt(n))), 
                width=.2,
                position=position_dodge(0.05))+
  ylim(0,10)+
  labs(
    title = 'EFA Factors',
    x = '',
    y = 'Number of Factors',
  )+
  theme_minimal()

ci_plt1;ci_plt2;ci_plt3;ci_plt4

Plotting the distribution of values

# srmr/rmsea
avg_rmsea = round(mean(cfaboot_df$rmsea),3)
sd_rmsea = round(sd(cfaboot_df$rmsea),3)
avg_srmr = round(mean(cfaboot_df$srmr),3)
sd_srmr = round(sd(cfaboot_df$srmr),3)

plt1 <- cfaboot_df %>% 
  gather(key = "FitIndex", value = "Statistic",
         srmr,rmsea) %>% 
  ggplot(aes(x =FitIndex, y = Statistic, fill = FitIndex, color=FitIndex)) +
  ggdist::stat_halfeye(adjust = .5, width = .7, .width = 0, justification = -.2, 
                       point_colour = NA, alpha = .5) +
  geom_boxplot(width = .2, outlier.shape = NA, alpha = .3) + 
  geom_jitter(width = .05, alpha = .5) +
  theme_minimal()+
  labs(
    title = 'CFA: RMSEA & SRMR',
    subtitle = paste("Mean RMSEA:",avg_rmsea, "(SD:",sd_srmr,")",
                     "Mean SRMR:",avg_srmr, "(SD:",sd_srmr,")"),
    x = 'Fit Stats',
    y = 'Type',
  )

# cfi/tli
avg_cfi = round(mean(cfaboot_df$cfi),3)
sd_cfi = round(sd(cfaboot_df$cfi),3)
avg_tli = round(mean(cfaboot_df$tli),3)
sd_tli = round(sd(cfaboot_df$tli),3)

plt2 = cfaboot_df %>% 
  gather(key = "FitIndex", value = "Statistic",
         cfi,tli) %>% 
  ggplot(aes(x =FitIndex, y = Statistic, fill = FitIndex, color=FitIndex)) +
  ggdist::stat_halfeye(adjust = .5, width = .7, .width = 0, justification = -.2, 
                       point_colour = NA, alpha = .5) +
  geom_boxplot(width = .2, outlier.shape = NA, alpha = .3) + 
  geom_jitter(width = .05, alpha = .5) +
  theme_minimal()+
  labs(
    title = 'CFA: CFI & TLI',
    subtitle = paste("Mean CFI:",avg_cfi, "(SD:",sd_cfi,")",
                     "Mean TLI:",avg_tli, "(SD:",sd_tli,")"),
    x = 'Fit Stats',
    y = 'Type',
  )

# aic/bic
avg_aic = round(mean(cfaboot_df$aic),2)
sd_aic = round(sd(cfaboot_df$aic),2)
avg_bic = round(mean(cfaboot_df$bic),2)
sd_bic = round(sd(cfaboot_df$bic),2)

plt3 = cfaboot_df %>% 
  gather(key = "FitIndex", value = "Statistic",
         aic,bic) %>% 
  ggplot(aes(x =FitIndex, y = Statistic, fill = FitIndex, color=FitIndex)) +
  ggdist::stat_halfeye(adjust = .5, width = .7, .width = 0, justification = -.2, 
                       point_colour = NA, alpha = .5) +
  geom_boxplot(width = .2, outlier.shape = NA, alpha = .3) + 
  geom_jitter(width = .05, alpha = .5) +
  theme_minimal()+
  labs(
    title = 'CFA: AIC & BIC',
    subtitle = paste("Mean AIC:",avg_aic, "(SD:",sd_aic,")",
                     "Mean BIC:",avg_bic, "(SD:",sd_bic,")"),
    x = 'Fit Stats',
    y = 'Type',
  )


avg = round(mean(resampled_res$Factors),1)
minimum = min(resampled_res$Factors)
maximum = max(resampled_res$Factors)

plt4 = resampled_res %>%
  ggplot(aes(x ="", y = Factors)) +
  ggdist::stat_halfeye(adjust = .5, width = .7, .width = 0, justification = -.2, 
                       point_colour = NA, alpha = .5) +
  geom_jitter(width = .05, alpha = .5) +
  theme_minimal()+
  labs(
    title = 'EFA: Parallel Analysis Recommended Factors',
    subtitle = paste("Mean:",avg," [Min:", minimum, "Max:", maximum,"]"),
    x = 'Fit Stats',
    y = 'Type',
  )

plt1;plt2;plt3;plt4

9.3 Invariance for sex at birth

sex_config <- cfa(model = lsem_model, data = abcd_df2, group = 'sex', 
                      estimator = "ML", std.lv = FALSE, meanstructure = TRUE)

model_parameters(sex_config, standardize = TRUE)

## # Loading
## 
## Link                                                             | Coefficient |   SE |       95% CI |     z |      p | Group
## -----------------------------------------------------------------------------------------------------------------------------
## Avoid_Insula_r2 =~ AWin_v_Neut_R_Ins_r2                          |        0.72 | 0.04 | [0.65, 0.79] | 20.15 | < .001 |  1.00
## Avoid_Insula_r2 =~ BWin_v_Neut_R_Ins_r2                          |        0.60 | 0.05 | [0.51, 0.69] | 12.64 | < .001 |  1.00
## Avoid_Insula_r2 =~ ALose_v_Neut_L_Ins_r2                         |        0.71 | 0.04 | [0.63, 0.79] | 17.47 | < .001 |  1.00
## Avoid_Insula_r2 =~ ALose_v_Neut_R_Ins_r2                         |        0.95 | 0.01 | [0.92, 0.98] | 66.11 | < .001 |  1.00
## Avoid_Insula_r2 =~ BLose_v_Neut_L_Ins_r2                         |        0.65 | 0.05 | [0.55, 0.74] | 13.83 | < .001 |  1.00
## Avoid_Insula_r2 =~ BLose_v_Neut_R_Ins_r2 (ALose_v_Neut_R_Ins_r2) |        0.92 | 0.02 | [0.89, 0.96] | 56.83 | < .001 |  1.00
## Appr_NAcc_r2 =~ AWin_v_Neut_L_NAc_r2                             |        0.47 | 0.06 | [0.35, 0.58] |  8.06 | < .001 |  1.00
## Appr_NAcc_r2 =~ AWin_v_Neut_R_NAc_r2                             |        0.50 | 0.06 | [0.38, 0.63] |  7.80 | < .001 |  1.00
## Appr_NAcc_r2 =~ BWin_v_Neut_L_NAc_r2                             |        0.68 | 0.05 | [0.58, 0.77] | 14.13 | < .001 |  1.00
## Appr_NAcc_r2 =~ BWin_v_Neut_R_NAc_r2 (AWin_v_Neut_R_NAc_r2)      |        0.66 | 0.05 | [0.55, 0.76] | 12.59 | < .001 |  1.00
## Appr_NAcc_r2 =~ BWin_v_BLose_L_NAc_r2                            |        0.74 | 0.05 | [0.64, 0.83] | 15.25 | < .001 |  1.00
## Appr_NAcc_r2 =~ BWin_v_BLose_R_NAc_r2                            |        0.70 | 0.05 | [0.60, 0.80] | 13.61 | < .001 |  1.00
## Avoid_Insula_r1 =~ AWin_v_Neut_R_Ins_r1                          |        0.67 | 0.04 | [0.60, 0.75] | 17.34 | < .001 |  1.00
## Avoid_Insula_r1 =~ BWin_v_Neut_R_Ins_r1                          |        0.58 | 0.05 | [0.48, 0.67] | 11.86 | < .001 |  1.00
## Avoid_Insula_r1 =~ ALose_v_Neut_L_Ins_r1                         |        0.69 | 0.04 | [0.60, 0.77] | 15.84 | < .001 |  1.00
## Avoid_Insula_r1 =~ ALose_v_Neut_R_Ins_r1                         |        0.93 | 0.02 | [0.90, 0.97] | 54.63 | < .001 |  1.00
## Avoid_Insula_r1 =~ BLose_v_Neut_L_Ins_r1                         |        0.73 | 0.04 | [0.65, 0.80] | 18.82 | < .001 |  1.00
## Avoid_Insula_r1 =~ BLose_v_Neut_R_Ins_r1 (ALose_v_Neut_R_Ins_r1) |        0.90 | 0.02 | [0.87, 0.94] | 46.94 | < .001 |  1.00
## Appr_NAcc_r1 =~ AWin_v_Neut_L_NAc_r1                             |        0.59 | 0.06 | [0.48, 0.70] | 10.32 | < .001 |  1.00
## Appr_NAcc_r1 =~ AWin_v_Neut_R_NAc_r1                             |        0.55 | 0.06 | [0.42, 0.67] |  8.42 | < .001 |  1.00
## Appr_NAcc_r1 =~ BWin_v_Neut_L_NAc_r1 (AWin_v_Neut_L_NAc_r1)      |        0.75 | 0.05 | [0.66, 0.84] | 15.88 | < .001 |  1.00
## Appr_NAcc_r1 =~ BWin_v_Neut_R_NAc_r1                             |        0.72 | 0.05 | [0.62, 0.81] | 14.36 | < .001 |  1.00
## Appr_NAcc_r1 =~ BWin_v_BLose_L_NAc_r1                            |        0.73 | 0.05 | [0.63, 0.82] | 15.01 | < .001 |  1.00
## Appr_NAcc_r1 =~ BWin_v_BLose_R_NAc_r1                            |        0.56 | 0.06 | [0.44, 0.68] |  9.15 | < .001 |  1.00
## Avoid_Insula_r2 =~ AWin_v_Neut_R_Ins_r2                          |        0.62 | 0.04 | [0.54, 0.70] | 15.62 | < .001 |  2.00
## Avoid_Insula_r2 =~ BWin_v_Neut_R_Ins_r2                          |        0.54 | 0.05 | [0.45, 0.63] | 11.32 | < .001 |  2.00
## Avoid_Insula_r2 =~ ALose_v_Neut_L_Ins_r2                         |        0.57 | 0.05 | [0.47, 0.68] | 10.77 | < .001 |  2.00
## Avoid_Insula_r2 =~ ALose_v_Neut_R_Ins_r2                         |        0.94 | 0.02 | [0.91, 0.98] | 52.34 | < .001 |  2.00
## Avoid_Insula_r2 =~ BLose_v_Neut_L_Ins_r2                         |        0.60 | 0.05 | [0.50, 0.70] | 11.67 | < .001 |  2.00
## Avoid_Insula_r2 =~ BLose_v_Neut_R_Ins_r2 (ALose_v_Neut_R_Ins_r2) |        0.92 | 0.02 | [0.89, 0.96] | 48.52 | < .001 |  2.00
## Appr_NAcc_r2 =~ AWin_v_Neut_L_NAc_r2                             |        0.49 | 0.06 | [0.38, 0.60] |  8.55 | < .001 |  2.00
## Appr_NAcc_r2 =~ AWin_v_Neut_R_NAc_r2                             |        0.51 | 0.06 | [0.38, 0.64] |  7.84 | < .001 |  2.00
## Appr_NAcc_r2 =~ BWin_v_Neut_L_NAc_r2                             |        0.68 | 0.05 | [0.59, 0.77] | 14.61 | < .001 |  2.00
## Appr_NAcc_r2 =~ BWin_v_Neut_R_NAc_r2 (AWin_v_Neut_R_NAc_r2)      |        0.73 | 0.05 | [0.64, 0.82] | 15.71 | < .001 |  2.00
## Appr_NAcc_r2 =~ BWin_v_BLose_L_NAc_r2                            |        0.72 | 0.05 | [0.62, 0.81] | 15.13 | < .001 |  2.00
## Appr_NAcc_r2 =~ BWin_v_BLose_R_NAc_r2                            |        0.72 | 0.05 | [0.62, 0.81] | 15.16 | < .001 |  2.00
## Avoid_Insula_r1 =~ AWin_v_Neut_R_Ins_r1                          |        0.67 | 0.04 | [0.59, 0.74] | 17.31 | < .001 |  2.00
## Avoid_Insula_r1 =~ BWin_v_Neut_R_Ins_r1                          |        0.62 | 0.04 | [0.53, 0.70] | 13.86 | < .001 |  2.00
## Avoid_Insula_r1 =~ ALose_v_Neut_L_Ins_r1                         |        0.71 | 0.04 | [0.63, 0.79] | 17.64 | < .001 |  2.00
## Avoid_Insula_r1 =~ ALose_v_Neut_R_Ins_r1                         |        0.96 | 0.01 | [0.93, 0.99] | 71.93 | < .001 |  2.00
## Avoid_Insula_r1 =~ BLose_v_Neut_L_Ins_r1                         |        0.69 | 0.04 | [0.61, 0.77] | 16.53 | < .001 |  2.00
## Avoid_Insula_r1 =~ BLose_v_Neut_R_Ins_r1 (ALose_v_Neut_R_Ins_r1) |        0.92 | 0.02 | [0.89, 0.95] | 55.81 | < .001 |  2.00
## Appr_NAcc_r1 =~ AWin_v_Neut_L_NAc_r1                             |        0.51 | 0.06 | [0.40, 0.62] |  8.96 | < .001 |  2.00
## Appr_NAcc_r1 =~ AWin_v_Neut_R_NAc_r1                             |        0.56 | 0.06 | [0.44, 0.69] |  8.75 | < .001 |  2.00
## Appr_NAcc_r1 =~ BWin_v_Neut_L_NAc_r1 (AWin_v_Neut_L_NAc_r1)      |        0.71 | 0.05 | [0.60, 0.81] | 13.68 | < .001 |  2.00
## Appr_NAcc_r1 =~ BWin_v_Neut_R_NAc_r1                             |        0.69 | 0.05 | [0.58, 0.79] | 12.88 | < .001 |  2.00
## Appr_NAcc_r1 =~ BWin_v_BLose_L_NAc_r1                            |        0.69 | 0.05 | [0.59, 0.79] | 12.98 | < .001 |  2.00
## Appr_NAcc_r1 =~ BWin_v_BLose_R_NAc_r1                            |        0.57 | 0.06 | [0.45, 0.69] |  9.28 | < .001 |  2.00
## 
## # Correlation
## 
## Link                                         | Coefficient |   SE |        95% CI |         z |      p | Group
## --------------------------------------------------------------------------------------------------------------
## AWin_v_Neut_L_NAc_r1 ~~ BWin_v_Neut_L_NAc_r1 |        0.89 | 0.02 | [ 0.85, 0.93] |     45.66 | < .001 |  1.00
## AWin_v_Neut_L_NAc_r2 ~~ BWin_v_Neut_L_NAc_r2 |        0.85 | 0.02 | [ 0.81, 0.90] |     36.10 | < .001 |  1.00
## AWin_v_Neut_R_NAc_r1 ~~ BWin_v_Neut_R_NAc_r1 |        0.85 | 0.02 | [ 0.80, 0.90] |     34.33 | < .001 |  1.00
## AWin_v_Neut_R_NAc_r2 ~~ BWin_v_Neut_R_NAc_r2 |        0.88 | 0.02 | [ 0.84, 0.92] |     46.25 | < .001 |  1.00
## AWin_v_Neut_R_Ins_r1 ~~ BWin_v_Neut_R_Ins_r1 |        0.76 | 0.03 | [ 0.69, 0.82] |     22.45 | < .001 |  1.00
## AWin_v_Neut_R_Ins_r2 ~~ BWin_v_Neut_R_Ins_r2 |        0.83 | 0.02 | [ 0.78, 0.88] |     33.32 | < .001 |  1.00
## Avoid_Insula_r2 ~~ Appr_NAcc_r2              |       -0.11 | 0.09 | [-0.28, 0.06] |     -1.30 | 0.195  |  1.00
## Avoid_Insula_r2 ~~ Avoid_Insula_r1           |   -2.95e-03 | 0.08 | [-0.16, 0.16] |     -0.04 | 0.971  |  1.00
## Avoid_Insula_r2 ~~ Appr_NAcc_r1              |        0.03 | 0.09 | [-0.14, 0.19] |      0.30 | 0.768  |  1.00
## Appr_NAcc_r2 ~~ Avoid_Insula_r1              |        0.10 | 0.09 | [-0.07, 0.27] |      1.13 | 0.257  |  1.00
## Appr_NAcc_r2 ~~ Appr_NAcc_r1                 |        0.19 | 0.09 | [ 0.02, 0.37] |      2.13 | 0.033  |  1.00
## Avoid_Insula_r1 ~~ Appr_NAcc_r1              |       -0.01 | 0.09 | [-0.18, 0.16] |     -0.15 | 0.882  |  1.00
## AWin_v_Neut_L_NAc_r1 ~~ BWin_v_Neut_L_NAc_r1 |        0.91 | 0.02 | [ 0.88, 0.94] |     57.79 | < .001 |  2.00
## AWin_v_Neut_L_NAc_r2 ~~ BWin_v_Neut_L_NAc_r2 |        0.89 | 0.02 | [ 0.85, 0.92] |     47.77 | < .001 |  2.00
## AWin_v_Neut_R_NAc_r1 ~~ BWin_v_Neut_R_NAc_r1 |        0.84 | 0.03 | [ 0.79, 0.89] |     32.12 | < .001 |  2.00
## AWin_v_Neut_R_NAc_r2 ~~ BWin_v_Neut_R_NAc_r2 |        0.88 | 0.02 | [ 0.84, 0.92] |     42.55 | < .001 |  2.00
## AWin_v_Neut_R_Ins_r1 ~~ BWin_v_Neut_R_Ins_r1 |        0.81 | 0.03 | [ 0.76, 0.86] |     31.02 | < .001 |  2.00
## AWin_v_Neut_R_Ins_r2 ~~ BWin_v_Neut_R_Ins_r2 |        0.84 | 0.02 | [ 0.80, 0.88] |     36.88 | < .001 |  2.00
## Avoid_Insula_r2 ~~ Appr_NAcc_r2              |        0.24 | 0.08 | [ 0.08, 0.40] |      2.89 | 0.004  |  2.00
## Avoid_Insula_r2 ~~ Avoid_Insula_r1           |        0.04 | 0.08 | [-0.12, 0.19] |      0.45 | 0.654  |  2.00
## Avoid_Insula_r2 ~~ Appr_NAcc_r1              |        0.04 | 0.09 | [-0.13, 0.21] |      0.49 | 0.622  |  2.00
## Appr_NAcc_r2 ~~ Avoid_Insula_r1              |   -6.41e-04 | 0.09 | [-0.17, 0.17] | -7.52e-03 | 0.994  |  2.00
## Appr_NAcc_r2 ~~ Appr_NAcc_r1                 |        0.15 | 0.09 | [-0.03, 0.33] |      1.66 | 0.097  |  2.00
## Avoid_Insula_r1 ~~ Appr_NAcc_r1              |        0.07 | 0.09 | [-0.10, 0.24] |      0.80 | 0.423  |  2.00

round(
  fitmeasures(
    sex_config, fit.measures = c("chisq","df","pvalue","rmsea", "srmr", "tli", "cfi")
    ), digits=2)

##   chisq      df  pvalue   rmsea    srmr     tli     cfi 
## 2444.67  484.00    0.00    0.15    0.11    0.73    0.76

Output parameters for the model

sex_params = data.frame(parameters(sex_config, standardize = T)) %>% 
  slice(1:29) %>% 
  select(-c("z","Component","Group","CI_low","CI_high")) %>% 
  rename("Fixed" = Label, "β" = Coefficient)

sex_params$p <- if_else(sex_params$p < .001, "< .001", 
                           if_else(sex_params$p < .01, "< .01", 
                                   if_else(sex_params$p < .05, "< .05", "> .05")))
sex_params[,4:5] <- round(sex_params[,c(4:5)],2)

# Report table
kable(sex_params, booktabs = TRUE) %>%
  kable_styling(font_size = 12,position = 'center',html_font = "Times New Roman")

To	Operator	From	β	SE	p	Fixed
Avoid_Insula_r2	=~	AWin_v_Neut_R_Ins_r2	0.72	0.04	< .001
Avoid_Insula_r2	=~	BWin_v_Neut_R_Ins_r2	0.60	0.05	< .001
Avoid_Insula_r2	=~	ALose_v_Neut_L_Ins_r2	0.71	0.04	< .001
Avoid_Insula_r2	=~	ALose_v_Neut_R_Ins_r2	0.95	0.01	< .001
Avoid_Insula_r2	=~	BLose_v_Neut_L_Ins_r2	0.65	0.05	< .001
Avoid_Insula_r2	=~	BLose_v_Neut_R_Ins_r2	0.92	0.02	< .001	ALose_v_Neut_R_Ins_r2
Appr_NAcc_r2	=~	AWin_v_Neut_L_NAc_r2	0.47	0.06	< .001
Appr_NAcc_r2	=~	AWin_v_Neut_R_NAc_r2	0.50	0.06	< .001
Appr_NAcc_r2	=~	BWin_v_Neut_L_NAc_r2	0.68	0.05	< .001
Appr_NAcc_r2	=~	BWin_v_Neut_R_NAc_r2	0.66	0.05	< .001	AWin_v_Neut_R_NAc_r2
Appr_NAcc_r2	=~	BWin_v_BLose_L_NAc_r2	0.74	0.05	< .001
Appr_NAcc_r2	=~	BWin_v_BLose_R_NAc_r2	0.70	0.05	< .001
Avoid_Insula_r1	=~	AWin_v_Neut_R_Ins_r1	0.67	0.04	< .001
Avoid_Insula_r1	=~	BWin_v_Neut_R_Ins_r1	0.58	0.05	< .001
Avoid_Insula_r1	=~	ALose_v_Neut_L_Ins_r1	0.69	0.04	< .001
Avoid_Insula_r1	=~	ALose_v_Neut_R_Ins_r1	0.93	0.02	< .001
Avoid_Insula_r1	=~	BLose_v_Neut_L_Ins_r1	0.73	0.04	< .001
Avoid_Insula_r1	=~	BLose_v_Neut_R_Ins_r1	0.90	0.02	< .001	ALose_v_Neut_R_Ins_r1
Appr_NAcc_r1	=~	AWin_v_Neut_L_NAc_r1	0.59	0.06	< .001
Appr_NAcc_r1	=~	AWin_v_Neut_R_NAc_r1	0.55	0.06	< .001
Appr_NAcc_r1	=~	BWin_v_Neut_L_NAc_r1	0.75	0.05	< .001	AWin_v_Neut_L_NAc_r1
Appr_NAcc_r1	=~	BWin_v_Neut_R_NAc_r1	0.72	0.05	< .001
Appr_NAcc_r1	=~	BWin_v_BLose_L_NAc_r1	0.73	0.05	< .001
Appr_NAcc_r1	=~	BWin_v_BLose_R_NAc_r1	0.56	0.06	< .001
AWin_v_Neut_L_NAc_r1	~~	BWin_v_Neut_L_NAc_r1	0.89	0.02	< .001
AWin_v_Neut_L_NAc_r2	~~	BWin_v_Neut_L_NAc_r2	0.85	0.02	< .001
AWin_v_Neut_R_NAc_r1	~~	BWin_v_Neut_R_NAc_r1	0.85	0.02	< .001
AWin_v_Neut_R_NAc_r2	~~	BWin_v_Neut_R_NAc_r2	0.88	0.02	< .001
AWin_v_Neut_R_Ins_r1	~~	BWin_v_Neut_R_Ins_r1	0.76	0.03	< .001

ANOVA comparing the strict CFA model versus the sex configural CFA model, model improve or not?

anova(heldout_cfa, sex_config)

## Chi-Squared Difference Test
## 
##              Df     AIC     BIC  Chisq Chisq diff Df diff Pr(>Chisq)   
## heldout_cfa 240 -7926.8 -7603.4 2133.0                                 
## sex_config  484 -7884.7 -7253.4 2444.7     311.66     244   0.002202 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

9.4 Effect of ABCD N on model fits

# combined data
combined_abcd = rbind(abcd_df[,-58],abcd_df2)

# set size
min = 50
max = 1000
interval = 10

# matrix 
out <- as.data.frame(matrix(NA, ncol = 12, nrow = length(seq(min,max,interval))))
colnames(out) <- c("N","χ2","DF","p-value", "RMSEA", "SRMR", "TLI","CFI", "AIC", "BIC","EFA_Factors","BIC2")

# loop
counter = 0
set.seed(112233)
for (size in seq(min, max, interval)) {
  counter = counter + 1
  sub_df <- sample_n(tbl = combined_abcd[,mod_vars], size = size, replace = TRUE)
  
  # cfa fit
  full_sample_cfa <- cfa(model = mid_model, data = sub_df,
                         estimator = "ML", std.lv = FALSE, meanstructure = TRUE, check.gradient = FALSE)
  # efa factors check
  n_fact <- nScree(x=sub_df,model="factors")
  
  
  # save outputs
  out[counter,1] <- size
  out[counter,2:8] <- round(data.matrix(
    fitmeasures(full_sample_cfa, fit.measures = c("chisq","df","pvalue","rmsea", "srmr", "tli", "cfi"))), digits=2)
  out[counter,9] <- round(AIC(full_sample_cfa),0)
  out[counter,10] <- round(BIC(full_sample_cfa),0)
  out[counter,11] <- n_fact$Components[3] # parallel analysis
  out[counter,12] <- round(data.matrix(
    fitmeasures(full_sample_cfa, fit.measures = c("bic2"))), digits=2)
  
}

ggplot(out, aes(x = N)) +
  geom_line(aes(y = RMSEA, color = "RMSEA")) +
  geom_line(aes(y = SRMR, color = "SRMR")) +
  scale_color_manual(values = c("RMSEA" = "blue", "SRMR" = "red")) +
  scale_y_continuous(limits = c(0,1), breaks = seq(0,1, by = .2))+
  labs(x = "Sample Size (N)", y = "RMSEA & SRMR") +
  theme_minimal()

ggplot(out, aes(x = N)) +
  geom_line(aes(y = TLI, color = "TLI")) +
  geom_line(aes(y = CFI, color = "CFI")) +
  scale_color_manual(values = c("TLI" = "blue", "CFI" = "red")) +
  labs(x = "Sample Size (N)", y = "TLI & CFI") +
  scale_y_continuous(limits = c(0,1), breaks = seq(0,1, by = .2))+
  theme_minimal()

ggplot(out, aes(x = N)) +
  geom_line(aes(y = AIC, color = "AIC")) +
  geom_line(aes(y = BIC, color = "BIC")) +
  scale_color_manual(values = c("AIC" = "blue", "BIC" = "red")) +
  labs(x = "Sample Size (N)", y = "AIC, BIC") +
  xlim(min,max)+
  theme_minimal()

ggplot(out, aes(x = N)) +
  geom_line(aes(y = EFA_Factors, color = "EFA_Factors")) +
  labs(x = "Sample Size (N)", y = "Parallel Analysis: N Factors") +
  scale_y_continuous(limits = c(1,10), breaks = seq(1,10, by = 1))+
  xlim(min,max)+
  guides(color = "none")+
  theme_minimal()

layout(t(1:2))
semPaths(sex_config,
         color = "lightgrey",
         theme="colorblind",
         whatLabels = "std",
         style = "lisrel",
         sizeLat = 6,
         sizeLat2 =6,
         sizeMan = 8,
         edge.color = "steelblue",
         edge.label.cex = 1.2,
         label.cex = 1.2,
         rotation = 4,
         layout = "tree2",
         intercepts = FALSE,
         residuals = FALSE,
         #residScale = 10,
         curve = 2,
         title = T,
         title.color = "black",
         cardinal = "lat cov",
         curvePivot = T,
         nCharNodes = 6,
         #nodeLabels = label,
         mar = c(3,4,3,4))

10 Posthoc Checks

The posthoc checks include the correlation matrices separated by runs for the model relevant variables. As well as run-by-run correlation + distribution plots across samples

10.1 Pairwise scatter plots run1 run 2

10.1.1 ABCD

abcd_run <- pivot_longer(abcd_df[,mod_vars], 
                        cols = matches("_r[1-2]$"), 
                        names_to = c(".value", "Run"), 
                        names_pattern = "(.*)_(r[1-2])$")

abcd_r1 = abcd_run %>% 
  filter(Run == 'r1') %>% 
  select(matches(gsub("_r[1-2]$", "", mod_vars))) 
abcd_r2 = abcd_run %>% 
  filter(Run == 'r2') %>% 
  select(matches(gsub("_r[1-2]$", "", mod_vars))) 

corrplot(cor(abcd_r1), method = "color", tl.pos = "ld", type = "lower", tl.cex = .6, title = "ABCD Run 1", mar = c(0,0,1,0))

corrplot(cor(abcd_r2), method = "color", tl.pos = "ld", type = "lower", tl.cex = .6, title = "ABCD Run 2", mar = c(0,0,1,0))

label_nacc = c("AWin_v_Neut_L_NAc_r1","BWin_v_Neut_L_NAc_r1","AWin_v_Neut_L_NAc_r2","BWin_v_Neut_L_NAc_r2")
label_ins = c("AWin_v_Neut_L_Ins_r1","BWin_v_Neut_L_Ins_r1","AWin_v_Neut_L_Ins_r2","BWin_v_Neut_L_Ins_r2")

ggpairs(abcd_df[,label_nacc]) + theme_minimal()

ggpairs(abcd_df[,label_ins]) + theme_minimal()

10.1.2 AHRB

ahrb_run <- pivot_longer(ahrb_df[,mod_vars], 
                        cols = matches("_r[1-2]$"), 
                        names_to = c(".value", "Run"), 
                        names_pattern = "(.*)_(r[1-2])$")
ahrb_r1 = ahrb_run %>% 
  filter(Run == 'r1') %>% 
  select(matches(gsub("_r[1-2]$", "", mod_vars))) 
ahrb_r2 = ahrb_run %>% 
  filter(Run == 'r2') %>% 
  select(matches(gsub("_r[1-2]$", "", mod_vars))) 

corrplot(cor(ahrb_r1), method = "color", tl.pos = "ld", type = "lower", tl.cex = .6, title = "AHRB Run 1", mar = c(0,0,1,0))

corrplot(cor(ahrb_r2), method = "color", tl.pos = "ld", type = "lower", tl.cex = .6, title = "AHRB Run 1", mar = c(0,0,1,0))

ggpairs(ahrb_df[,label_nacc]) + theme_minimal()

ggpairs(ahrb_df[,label_ins]) + theme_minimal()

10.1.3 MLS

mls_run <- pivot_longer(mls_df[,mod_vars], 
                        cols = matches("_r[1-2]$"), 
                        names_to = c(".value", "Run"), 
                        names_pattern = "(.*)_(r[1-2])$")

mls_r1 = mls_run %>% 
  filter(Run == 'r1') %>% 
  select(matches(gsub("_r[1-2]$", "", mod_vars))) 
mls_r2 = mls_run %>% 
  filter(Run == 'r2') %>% 
  select(matches(gsub("_r[1-2]$", "", mod_vars))) 

corrplot(cor(mls_r1), method = "color", tl.pos = "ld", type = "lower", tl.cex = .6, title = "MLS Run 1", mar = c(0,0,1,0))

corrplot(cor(mls_r2), method = "color", tl.pos = "ld", type = "lower", tl.cex = .6, title = "MLS Run 1", mar = c(0,0,1,0))

ggpairs(mls_df[,label_nacc]) + theme_minimal()

ggpairs(mls_df[,label_ins]) + theme_minimal()

11 Reproducing CFA/EFA models

Providing the covariance matrices, the means and standard deviations for the manifest [28] model variables so the above CFA/ESEM/EFA data can be reproduced for modeling purposes. Doing separately for the ABCD, AHRB and MLS.

11.1 ABCD

11.1.1 Primary

The covariance matrices for the [28] manifest variables for the primary ABCD primary dataset that has N observations: 346

abcd_cov = cov(abcd_df[,mod_vars])
abcd_means = data.frame(means = colMeans(abcd_df[,mod_vars]))
abcd_sd = data.frame(sds = sapply(abcd_df[,mod_vars], sd))
abcd_dat = cbind(abcd_cov, abcd_means, abcd_sd)

kable(abcd_dat, booktabs = TRUE) %>%
  kable_styling(font_size = 12,position = 'center',html_font = "Times New Roman")

	AWin_v_Neut_L_NAc_r1	AWin_v_Neut_R_NAc_r1	AWin_v_Neut_L_NAc_r2	AWin_v_Neut_R_NAc_r2	BWin_v_Neut_L_NAc_r1	BWin_v_Neut_R_NAc_r1	BWin_v_Neut_L_NAc_r2	BWin_v_Neut_R_NAc_r2	BWin_v_BLose_L_NAc_r1	BWin_v_BLose_R_NAc_r1	BWin_v_BLose_L_NAc_r2	BWin_v_BLose_R_NAc_r2	AWin_v_Neut_R_Ins_r1	AWin_v_Neut_R_Ins_r2	BWin_v_Neut_R_Ins_r1	BWin_v_Neut_R_Ins_r2	ALose_v_Neut_L_Ins_r1	ALose_v_Neut_R_Ins_r1	ALose_v_Neut_L_Ins_r2	ALose_v_Neut_R_Ins_r2	BLose_v_Neut_L_Ins_r1	BLose_v_Neut_R_Ins_r1	BLose_v_Neut_L_Ins_r2	BLose_v_Neut_R_Ins_r2	BLose_v_BWin_L_Ins_r1	BLose_v_BWin_R_Ins_r1	BLose_v_BWin_L_Ins_r2	BLose_v_BWin_R_Ins_r2	means	sds
AWin_v_Neut_L_NAc_r1	0.0469046	0.0285755	0.0107462	0.0075053	0.0496735	0.0315054	0.0115552	0.0086345	0.0177351	0.0145264	0.0017099	0.0006396	0.0070571	0.0007951	0.0082449	0.0022187	0.0057611	0.0040562	0.0038046	0.0014276	0.0082268	0.0052281	0.0026212	0.0004063	-0.0032115	-0.0030222	-0.0008158	-0.0018121	0.1908035	0.2165747
AWin_v_Neut_R_NAc_r1	0.0285755	0.0491611	0.0104844	0.0085838	0.0318310	0.0540859	0.0107428	0.0092132	0.0138263	0.0247973	-0.0009862	-0.0026060	0.0057946	-0.0001806	0.0078146	-0.0009876	0.0049108	0.0035467	0.0014778	-0.0006833	0.0053311	0.0031306	0.0004617	-0.0021500	-0.0050712	-0.0046911	0.0020782	-0.0011609	0.2141618	0.2217229
AWin_v_Neut_L_NAc_r2	0.0107462	0.0104844	0.0538025	0.0360956	0.0155428	0.0158417	0.0554017	0.0364735	0.0090087	0.0101722	0.0172803	0.0137260	-0.0023718	0.0101334	-0.0017082	0.0086262	-0.0001920	-0.0033917	0.0045802	0.0043667	-0.0003119	-0.0035539	0.0050147	0.0027867	-0.0005740	-0.0018490	-0.0060251	-0.0058292	0.1317110	0.2319537
AWin_v_Neut_R_NAc_r2	0.0075053	0.0085838	0.0360956	0.0559332	0.0102704	0.0111368	0.0377373	0.0586475	0.0084975	0.0071565	0.0106380	0.0205423	-0.0026712	0.0111601	-0.0015589	0.0117221	-0.0006328	-0.0036175	0.0055201	0.0074140	-0.0010288	-0.0045315	0.0085010	0.0082806	-0.0018716	-0.0029784	-0.0015491	-0.0034429	0.1528757	0.2365021
BWin_v_Neut_L_NAc_r1	0.0496735	0.0318310	0.0155428	0.0102704	0.0672397	0.0442373	0.0178301	0.0122567	0.0332177	0.0254870	0.0046079	0.0025636	0.0082137	0.0010710	0.0125005	0.0025854	0.0050027	0.0026694	0.0058487	0.0020356	0.0075090	0.0039724	0.0048039	0.0013650	-0.0074021	-0.0085319	0.0004739	-0.0012182	0.2472283	0.2593061
BWin_v_Neut_R_NAc_r1	0.0315054	0.0540859	0.0158417	0.0111368	0.0442373	0.0744899	0.0173773	0.0128713	0.0232228	0.0408417	-0.0001210	-0.0025060	0.0074773	0.0015501	0.0125358	0.0008746	0.0051993	0.0026151	0.0025510	0.0005788	0.0062242	0.0022491	0.0017240	-0.0002838	-0.0082322	-0.0102913	0.0024868	-0.0011559	0.2759538	0.2729283
BWin_v_Neut_L_NAc_r2	0.0115552	0.0107428	0.0554017	0.0377373	0.0178301	0.0173773	0.0710702	0.0472304	0.0121880	0.0130547	0.0299180	0.0226341	-0.0028915	0.0092540	-0.0009813	0.0113122	-0.0022582	-0.0053464	0.0043987	0.0041749	-0.0021464	-0.0046593	0.0039661	0.0031526	-0.0033213	-0.0036827	-0.0115121	-0.0081517	0.1946185	0.2665900
BWin_v_Neut_R_NAc_r2	0.0086345	0.0092132	0.0364735	0.0586475	0.0122567	0.0128713	0.0472304	0.0770891	0.0108252	0.0103188	0.0192164	0.0362843	-0.0045415	0.0090401	-0.0031893	0.0127149	-0.0023822	-0.0060262	0.0048068	0.0045999	-0.0023903	-0.0064257	0.0075901	0.0063248	-0.0033301	-0.0032426	-0.0063787	-0.0063934	0.2159364	0.2776493
BWin_v_BLose_L_NAc_r1	0.0177351	0.0138263	0.0090087	0.0084975	0.0332177	0.0232228	0.0121880	0.0108252	0.0595915	0.0390343	0.0048770	0.0026138	0.0061007	0.0002451	0.0111626	0.0013230	-0.0040390	-0.0047019	0.0026587	0.0013854	-0.0050144	-0.0072450	0.0038621	0.0024282	-0.0153322	-0.0184076	0.0031111	0.0010937	0.1165867	0.2441138
BWin_v_BLose_R_NAc_r1	0.0145264	0.0247973	0.0101722	0.0071565	0.0254870	0.0408417	0.0130547	0.0103188	0.0390343	0.0666993	0.0044629	0.0009771	0.0058132	-0.0005350	0.0112383	-0.0004754	0.0007189	-0.0024777	-0.0000330	0.0002263	-0.0002651	-0.0045996	0.0002877	0.0008860	-0.0132882	-0.0158436	0.0033678	0.0013524	0.1269133	0.2582621
BWin_v_BLose_L_NAc_r2	0.0017099	-0.0009862	0.0172803	0.0106380	0.0046079	-0.0001210	0.0299180	0.0192164	0.0048770	0.0044629	0.0539756	0.0358264	-0.0044865	-0.0024166	-0.0061454	0.0006347	-0.0042539	-0.0051549	-0.0050674	-0.0079848	-0.0047009	-0.0035263	-0.0089000	-0.0111049	-0.0009539	0.0026196	-0.0141077	-0.0117427	0.0995347	0.2323266
BWin_v_BLose_R_NAc_r2	0.0006396	-0.0026060	0.0137260	0.0205423	0.0025636	-0.0025060	0.0226341	0.0362843	0.0026138	0.0009771	0.0358264	0.0658146	-0.0077536	-0.0033683	-0.0088023	-0.0000963	-0.0044098	-0.0077221	-0.0073681	-0.0102888	-0.0051406	-0.0066963	-0.0108464	-0.0137368	-0.0003078	0.0021007	-0.0147017	-0.0136469	0.0900116	0.2565436
AWin_v_Neut_R_Ins_r1	0.0070571	0.0057946	-0.0023718	-0.0026712	0.0082137	0.0074773	-0.0028915	-0.0045415	0.0061007	0.0058132	-0.0044865	-0.0077536	0.0309887	0.0027441	0.0337384	0.0008415	0.0118173	0.0176455	0.0057772	0.0045236	0.0127497	0.0169397	0.0068707	0.0056582	-0.0079752	-0.0168006	0.0043632	0.0048145	0.0223324	0.1760360
AWin_v_Neut_R_Ins_r2	0.0007951	-0.0001806	0.0101334	0.0111601	0.0010710	0.0015501	0.0092540	0.0090401	0.0002451	-0.0005350	-0.0024166	-0.0033683	0.0027441	0.0337152	0.0046278	0.0342678	0.0030018	0.0031538	0.0137985	0.0237889	0.0032919	0.0037941	0.0156703	0.0248026	0.0000100	-0.0008338	-0.0041371	-0.0094570	0.0323613	0.1836171
BWin_v_Neut_R_Ins_r1	0.0082449	0.0078146	-0.0017082	-0.0015589	0.0125005	0.0125358	-0.0009813	-0.0031893	0.0111626	0.0112383	-0.0061454	-0.0088023	0.0337384	0.0046278	0.0475069	0.0020512	0.0140522	0.0196118	0.0074508	0.0067638	0.0147761	0.0186314	0.0089099	0.0082765	-0.0144289	-0.0288779	0.0051212	0.0062178	0.0460838	0.2179608
BWin_v_Neut_R_Ins_r2	0.0022187	-0.0009876	0.0086262	0.0117221	0.0025854	0.0008746	0.0113122	0.0127149	0.0013230	-0.0004754	0.0006347	-0.0000963	0.0008415	0.0342678	0.0020512	0.0459887	0.0011391	0.0014669	0.0149094	0.0259120	0.0013758	0.0022502	0.0169921	0.0277472	0.0010135	0.0001991	-0.0101799	-0.0182306	0.0605520	0.2144497
ALose_v_Neut_L_Ins_r1	0.0057611	0.0049108	-0.0001920	-0.0006328	0.0050027	0.0051993	-0.0022582	-0.0023822	-0.0040390	0.0007189	-0.0042539	-0.0044098	0.0118173	0.0030018	0.0140522	0.0011391	0.0262837	0.0162721	0.0037921	0.0026887	0.0274271	0.0167423	0.0029713	0.0012839	0.0070421	0.0026917	0.0000513	0.0001522	0.0013844	0.1621224
ALose_v_Neut_R_Ins_r1	0.0040562	0.0035467	-0.0033917	-0.0036175	0.0026694	0.0026151	-0.0053464	-0.0060262	-0.0047019	-0.0024777	-0.0051549	-0.0077221	0.0176455	0.0031538	0.0196118	0.0014669	0.0162721	0.0263569	0.0046089	0.0035617	0.0169470	0.0264348	0.0056513	0.0038809	0.0059127	0.0068235	0.0026116	0.0024166	-0.0001705	0.1623482
ALose_v_Neut_L_Ins_r2	0.0038046	0.0014778	0.0045802	0.0055201	0.0058487	0.0025510	0.0043987	0.0048068	0.0026587	-0.0000330	-0.0050674	-0.0073681	0.0057772	0.0137985	0.0074508	0.0149094	0.0037921	0.0046089	0.0320629	0.0241134	0.0040885	0.0040090	0.0326100	0.0260545	-0.0028410	-0.0034409	0.0120117	0.0111523	0.0022428	0.1790612
ALose_v_Neut_R_Ins_r2	0.0014276	-0.0006833	0.0043667	0.0074140	0.0020356	0.0005788	0.0041749	0.0045999	0.0013854	0.0002263	-0.0079848	-0.0102888	0.0045236	0.0237889	0.0067638	0.0259120	0.0026887	0.0035617	0.0241134	0.0362162	0.0040557	0.0045849	0.0259845	0.0397169	-0.0016946	-0.0021804	0.0100201	0.0138075	0.0159653	0.1903056
BLose_v_Neut_L_Ins_r1	0.0082268	0.0053311	-0.0003119	-0.0010288	0.0075090	0.0062242	-0.0021464	-0.0023903	-0.0050144	-0.0002651	-0.0047009	-0.0051406	0.0127497	0.0032919	0.0147761	0.0013758	0.0274271	0.0169470	0.0040885	0.0040557	0.0359023	0.0227878	0.0026464	0.0028081	0.0141328	0.0080116	-0.0001483	0.0014369	0.0296705	0.1894790
BLose_v_Neut_R_Ins_r1	0.0052281	0.0031306	-0.0035539	-0.0045315	0.0039724	0.0022491	-0.0046593	-0.0064257	-0.0072450	-0.0045996	-0.0035263	-0.0066963	0.0169397	0.0037941	0.0186314	0.0022502	0.0167423	0.0264348	0.0040090	0.0045849	0.0227878	0.0362396	0.0045871	0.0052665	0.0115754	0.0176094	0.0012430	0.0030203	0.0293873	0.1903670
BLose_v_Neut_L_Ins_r2	0.0026212	0.0004617	0.0050147	0.0085010	0.0048039	0.0017240	0.0039661	0.0075901	0.0038621	0.0002877	-0.0089000	-0.0108464	0.0068707	0.0156703	0.0089099	0.0169921	0.0029713	0.0056513	0.0326100	0.0259845	0.0026464	0.0045871	0.0445186	0.0365596	-0.0046228	-0.0043250	0.0213947	0.0195758	0.0267197	0.2109944
BLose_v_Neut_R_Ins_r2	0.0004063	-0.0021500	0.0027867	0.0082806	0.0013650	-0.0002838	0.0031526	0.0063248	0.0024282	0.0008860	-0.0111049	-0.0137368	0.0056582	0.0248026	0.0082765	0.0277472	0.0012839	0.0038809	0.0260545	0.0397169	0.0028081	0.0052665	0.0365596	0.0567302	-0.0023877	-0.0030161	0.0174870	0.0289860	0.0391647	0.2381811
BLose_v_BWin_L_Ins_r1	-0.0032115	-0.0050712	-0.0005740	-0.0018716	-0.0074021	-0.0082322	-0.0033213	-0.0033301	-0.0153322	-0.0132882	-0.0009539	-0.0003078	-0.0079752	0.0000100	-0.0144289	0.0010135	0.0070421	0.0059127	-0.0028410	-0.0016946	0.0141328	0.0115754	-0.0046228	-0.0023877	0.0326114	0.0260075	-0.0037686	-0.0033991	-0.0231416	0.1805862
BLose_v_BWin_R_Ins_r1	-0.0030222	-0.0046911	-0.0018490	-0.0029784	-0.0085319	-0.0102913	-0.0036827	-0.0032426	-0.0184076	-0.0158436	0.0026196	0.0021007	-0.0168006	-0.0008338	-0.0288779	0.0001991	0.0026917	0.0068235	-0.0034409	-0.0021804	0.0080116	0.0176094	-0.0043250	-0.0030161	0.0260075	0.0464912	-0.0038841	-0.0032036	-0.0166879	0.2156181
BLose_v_BWin_L_Ins_r2	-0.0008158	0.0020782	-0.0060251	-0.0015491	0.0004739	0.0024868	-0.0115121	-0.0063787	0.0031111	0.0033678	-0.0141077	-0.0147017	0.0043632	-0.0041371	0.0051212	-0.0101799	0.0000513	0.0026116	0.0120117	0.0100201	-0.0001483	0.0012430	0.0213947	0.0174870	-0.0037686	-0.0038841	0.0382489	0.0276649	-0.0318671	0.1955734
BLose_v_BWin_R_Ins_r2	-0.0018121	-0.0011609	-0.0058292	-0.0034429	-0.0012182	-0.0011559	-0.0081517	-0.0063934	0.0010937	0.0013524	-0.0117427	-0.0136469	0.0048145	-0.0094570	0.0062178	-0.0182306	0.0001522	0.0024166	0.0111523	0.0138075	0.0014369	0.0030203	0.0195758	0.0289860	-0.0033991	-0.0032036	0.0276649	0.0472089	-0.0213931	0.2172761

11.1.2 Held-out

The covariance matrices for the [28] manifest variables for the primary ABCD held-out primary dataset that has N observations: 346

abcd_cov = cov(abcd_df2[,mod_vars])
abcd_means = data.frame(means = colMeans(abcd_df2[,mod_vars]))
abcd_sd = data.frame(sds = sapply(abcd_df2[,mod_vars], sd))
abcd_dat = cbind(abcd_cov, abcd_means, abcd_sd)

kable(abcd_dat, booktabs = TRUE) %>%
  kable_styling(font_size = 12,position = 'center',html_font = "Times New Roman")

	AWin_v_Neut_L_NAc_r1	AWin_v_Neut_R_NAc_r1	AWin_v_Neut_L_NAc_r2	AWin_v_Neut_R_NAc_r2	BWin_v_Neut_L_NAc_r1	BWin_v_Neut_R_NAc_r1	BWin_v_Neut_L_NAc_r2	BWin_v_Neut_R_NAc_r2	BWin_v_BLose_L_NAc_r1	BWin_v_BLose_R_NAc_r1	BWin_v_BLose_L_NAc_r2	BWin_v_BLose_R_NAc_r2	AWin_v_Neut_R_Ins_r1	AWin_v_Neut_R_Ins_r2	BWin_v_Neut_R_Ins_r1	BWin_v_Neut_R_Ins_r2	ALose_v_Neut_L_Ins_r1	ALose_v_Neut_R_Ins_r1	ALose_v_Neut_L_Ins_r2	ALose_v_Neut_R_Ins_r2	BLose_v_Neut_L_Ins_r1	BLose_v_Neut_R_Ins_r1	BLose_v_Neut_L_Ins_r2	BLose_v_Neut_R_Ins_r2	BLose_v_BWin_L_Ins_r1	BLose_v_BWin_R_Ins_r1	BLose_v_BWin_L_Ins_r2	BLose_v_BWin_R_Ins_r2	means	sds
AWin_v_Neut_L_NAc_r1	0.0557822	0.0328238	0.0103577	0.0123781	0.0590094	0.0334536	0.0120327	0.0151670	0.0219987	0.0091392	0.0010579	0.0031478	0.0092267	0.0013534	0.0101421	0.0003201	0.0089980	0.0067903	0.0012024	-0.0014333	0.0101401	0.0082772	0.0025947	-0.0008880	-0.0028023	-0.0018608	0.0003641	-0.0012158	0.1870375	0.2361825
AWin_v_Neut_R_NAc_r1	0.0328238	0.0502834	0.0121156	0.0109471	0.0365849	0.0513998	0.0134552	0.0126915	0.0157859	0.0172624	0.0035675	0.0028687	0.0074474	0.0042056	0.0101575	0.0036397	0.0079234	0.0061486	0.0010983	0.0023260	0.0087064	0.0072426	0.0036594	0.0044527	-0.0028994	-0.0029138	0.0014318	0.0008081	0.1929280	0.2242396
AWin_v_Neut_L_NAc_r2	0.0103577	0.0121156	0.0504855	0.0332557	0.0123084	0.0135529	0.0531619	0.0346970	0.0048155	-0.0000854	0.0187645	0.0115645	0.0006689	0.0152412	0.0031325	0.0152174	0.0014213	0.0026793	0.0064086	0.0069037	0.0047533	0.0046342	0.0074796	0.0078082	0.0031144	0.0014992	-0.0060852	-0.0074184	0.1327406	0.2246898
AWin_v_Neut_R_NAc_r2	0.0123781	0.0109471	0.0332557	0.0533766	0.0159560	0.0128082	0.0352576	0.0562140	0.0075531	0.0020428	0.0156202	0.0214021	0.0005579	0.0106537	0.0018469	0.0106818	0.0023347	0.0035697	0.0029643	0.0045745	0.0036346	0.0043161	0.0037857	0.0049233	0.0028223	0.0024663	-0.0049336	-0.0057624	0.1392594	0.2310337
BWin_v_Neut_L_NAc_r1	0.0590094	0.0365849	0.0123084	0.0159560	0.0742511	0.0444358	0.0145709	0.0194221	0.0341778	0.0161210	0.0032778	0.0053036	0.0081238	0.0025630	0.0117000	0.0024398	0.0097762	0.0057189	0.0017846	-0.0004638	0.0123790	0.0088295	0.0041501	0.0006532	-0.0045802	-0.0028661	0.0006565	-0.0017921	0.2473372	0.2724906
BWin_v_Neut_R_NAc_r1	0.0334536	0.0513998	0.0135529	0.0128082	0.0444358	0.0666411	0.0164957	0.0160194	0.0219556	0.0294405	0.0055008	0.0037052	0.0052696	0.0032777	0.0109874	0.0029417	0.0076393	0.0044721	-0.0004136	0.0007114	0.0092557	0.0062300	0.0034727	0.0035873	-0.0038508	-0.0047504	0.0012360	0.0006428	0.2560663	0.2581493
BWin_v_Neut_L_NAc_r2	0.0120327	0.0134552	0.0531619	0.0352576	0.0145709	0.0164957	0.0712003	0.0446830	0.0041074	-0.0015334	0.0341422	0.0208799	-0.0004682	0.0153285	0.0026302	0.0178436	0.0004656	0.0028777	0.0059108	0.0073961	0.0047400	0.0054424	0.0070289	0.0092493	0.0045908	0.0028025	-0.0088326	-0.0086037	0.1963026	0.2668338
BWin_v_Neut_R_NAc_r2	0.0151670	0.0126915	0.0346970	0.0562140	0.0194221	0.0160194	0.0446830	0.0732029	0.0074105	0.0019209	0.0238890	0.0367996	0.0006450	0.0100595	0.0019093	0.0118545	0.0018455	0.0042023	0.0023916	0.0055546	0.0035071	0.0059657	0.0033596	0.0068983	0.0025879	0.0040518	-0.0062887	-0.0049600	0.2053660	0.2705604
BWin_v_BLose_L_NAc_r1	0.0219987	0.0157859	0.0048155	0.0075531	0.0341778	0.0219556	0.0041074	0.0074105	0.0527428	0.0337899	0.0017921	0.0003303	0.0003300	0.0007942	0.0055499	-0.0012258	0.0026344	-0.0056921	0.0029335	0.0008208	0.0000575	-0.0068176	0.0048783	0.0016521	-0.0129595	-0.0123605	0.0030787	0.0028776	0.1105591	0.2296579
BWin_v_BLose_R_NAc_r1	0.0091392	0.0172624	-0.0000854	0.0020428	0.0161210	0.0294405	-0.0015334	0.0019209	0.0337899	0.0657161	0.0007081	-0.0024623	0.0015229	0.0029549	0.0052723	0.0021811	0.0006646	-0.0053785	0.0000005	-0.0001936	-0.0014059	-0.0081248	0.0028746	0.0019924	-0.0094846	-0.0133865	0.0013063	-0.0001931	0.1174726	0.2563515
BWin_v_BLose_L_NAc_r2	0.0010579	0.0035675	0.0187645	0.0156202	0.0032778	0.0055008	0.0341422	0.0238890	0.0017921	0.0007081	0.0536541	0.0327485	-0.0032445	0.0076854	-0.0028092	0.0124905	-0.0022080	-0.0000547	-0.0061143	-0.0024123	-0.0002123	0.0003634	-0.0088780	-0.0035380	0.0026691	0.0031658	-0.0186075	-0.0160306	0.0967118	0.2316335
BWin_v_BLose_R_NAc_r2	0.0031478	0.0028687	0.0115645	0.0214021	0.0053036	0.0037052	0.0208799	0.0367996	0.0003303	-0.0024623	0.0327485	0.0605793	-0.0006331	0.0067385	-0.0013061	0.0113458	-0.0017572	0.0009062	-0.0068303	-0.0024382	-0.0012260	0.0011681	-0.0093977	-0.0040142	0.0008684	0.0024744	-0.0177127	-0.0153662	0.0895159	0.2461286
AWin_v_Neut_R_Ins_r1	0.0092267	0.0074474	0.0006689	0.0005579	0.0081238	0.0052696	-0.0004682	0.0006450	0.0003300	0.0015229	-0.0032445	-0.0006331	0.0288019	0.0032436	0.0296436	0.0013967	0.0127495	0.0199767	0.0017589	0.0016056	0.0140959	0.0200807	0.0010925	0.0012005	-0.0040838	-0.0095549	-0.0014950	-0.0002033	0.0436888	0.1697111
AWin_v_Neut_R_Ins_r2	0.0013534	0.0042056	0.0152412	0.0106537	0.0025630	0.0032777	0.0153285	0.0100595	0.0007942	0.0029549	0.0076854	0.0067385	0.0032436	0.0407125	0.0031467	0.0429415	-0.0002537	0.0011212	0.0142389	0.0254462	0.0020435	0.0034180	0.0139632	0.0257095	0.0003642	0.0002746	-0.0099532	-0.0172335	0.0287176	0.2017734
BWin_v_Neut_R_Ins_r1	0.0101421	0.0101575	0.0031325	0.0018469	0.0117000	0.0109874	0.0026302	0.0019093	0.0055499	0.0052723	-0.0028092	-0.0013061	0.0296436	0.0031467	0.0404752	0.0008156	0.0135005	0.0211929	0.0019455	0.0010833	0.0144522	0.0213397	0.0022651	0.0013151	-0.0105741	-0.0191250	-0.0008615	0.0004937	0.0650519	0.2011844
BWin_v_Neut_R_Ins_r2	0.0003201	0.0036397	0.0152174	0.0106818	0.0024398	0.0029417	0.0178436	0.0118545	-0.0012258	0.0021811	0.0124905	0.0113458	0.0013967	0.0429415	0.0008156	0.0571385	-0.0017257	-0.0001909	0.0125136	0.0259028	0.0012974	0.0018790	0.0117596	0.0261484	0.0011225	0.0010651	-0.0202777	-0.0309919	0.0617752	0.2390366
ALose_v_Neut_L_Ins_r1	0.0089980	0.0079234	0.0014213	0.0023347	0.0097762	0.0076393	0.0004656	0.0018455	0.0026344	0.0006646	-0.0022080	-0.0017572	0.0127495	-0.0002537	0.0135005	-0.0017257	0.0280955	0.0192497	-0.0008413	-0.0031848	0.0280103	0.0192292	0.0002427	-0.0022845	0.0067962	0.0057389	-0.0028511	-0.0005667	0.0126571	0.1676170
ALose_v_Neut_R_Ins_r1	0.0067903	0.0061486	0.0026793	0.0035697	0.0057189	0.0044721	0.0028777	0.0042023	-0.0056921	-0.0053785	-0.0000547	0.0009062	0.0199767	0.0011212	0.0211929	-0.0001909	0.0192497	0.0312697	0.0005756	-0.0001818	0.0206426	0.0319157	0.0001193	-0.0008661	0.0074856	0.0107311	-0.0027063	-0.0006797	0.0127810	0.1768323
ALose_v_Neut_L_Ins_r2	0.0012024	0.0010983	0.0064086	0.0029643	0.0017846	-0.0004136	0.0059108	0.0023916	0.0029335	0.0000005	-0.0061143	-0.0068303	0.0017589	0.0142389	0.0019455	0.0125136	-0.0008413	0.0005756	0.0309195	0.0206730	0.0008849	0.0020439	0.0294992	0.0200747	-0.0004360	0.0000989	0.0083251	0.0075589	-0.0082046	0.1758394
ALose_v_Neut_R_Ins_r2	-0.0014333	0.0023260	0.0069037	0.0045745	-0.0004638	0.0007114	0.0073961	0.0055546	0.0008208	-0.0001936	-0.0024123	-0.0024382	0.0016056	0.0254462	0.0010833	0.0259028	-0.0031848	-0.0001818	0.0206730	0.0362689	-0.0007403	0.0028644	0.0190696	0.0353652	0.0010767	0.0017813	0.0069493	0.0094616	-0.0006945	0.1904439
BLose_v_Neut_L_Ins_r1	0.0101401	0.0087064	0.0047533	0.0036346	0.0123790	0.0092557	0.0047400	0.0035071	0.0000575	-0.0014059	-0.0002123	-0.0012260	0.0140959	0.0020435	0.0144522	0.0012974	0.0280103	0.0206426	0.0008849	-0.0007403	0.0372483	0.0266443	0.0008375	-0.0007733	0.0165010	0.0122002	-0.0048918	-0.0020770	0.0313804	0.1929982
BLose_v_Neut_R_Ins_r1	0.0082772	0.0072426	0.0046342	0.0043161	0.0088295	0.0062300	0.0054424	0.0059657	-0.0068176	-0.0081248	0.0003634	0.0011681	0.0200807	0.0034180	0.0213397	0.0018790	0.0192292	0.0319157	0.0020439	0.0028644	0.0266443	0.0424528	0.0005308	0.0010476	0.0129171	0.0211217	-0.0032761	-0.0008332	0.0201671	0.2060409
BLose_v_Neut_L_Ins_r2	0.0025947	0.0036594	0.0074796	0.0037857	0.0041501	0.0034727	0.0070289	0.0033596	0.0048783	0.0028746	-0.0088780	-0.0093977	0.0010925	0.0139632	0.0022651	0.0117596	0.0002427	0.0001193	0.0294992	0.0190696	0.0008375	0.0005308	0.0373787	0.0249292	-0.0017238	-0.0017350	0.0157495	0.0131637	0.0095677	0.1933357
BLose_v_Neut_R_Ins_r2	-0.0008880	0.0044527	0.0078082	0.0049233	0.0006532	0.0035873	0.0092493	0.0068983	0.0016521	0.0019924	-0.0035380	-0.0040142	0.0012005	0.0257095	0.0013151	0.0261484	-0.0022845	-0.0008661	0.0200747	0.0353652	-0.0007733	0.0010476	0.0249292	0.0445328	0.0007660	-0.0002689	0.0123456	0.0183780	0.0069049	0.2110280
BLose_v_BWin_L_Ins_r1	-0.0028023	-0.0028994	0.0031144	0.0028223	-0.0045802	-0.0038508	0.0045908	0.0025879	-0.0129595	-0.0094846	0.0026691	0.0008684	-0.0040838	0.0003642	-0.0105741	0.0011225	0.0067962	0.0074856	-0.0004360	0.0010767	0.0165010	0.0129171	-0.0017238	0.0007660	0.0351010	0.0234896	-0.0028515	-0.0003570	-0.0310202	0.1873527
BLose_v_BWin_R_Ins_r1	-0.0018608	-0.0029138	0.0014992	0.0024663	-0.0028661	-0.0047504	0.0028025	0.0040518	-0.0123605	-0.0133865	0.0031658	0.0024744	-0.0095549	0.0002746	-0.0191250	0.0010651	0.0057389	0.0107311	0.0000989	0.0017813	0.0122002	0.0211217	-0.0017350	-0.0002689	0.0234896	0.0402451	-0.0024206	-0.0013301	-0.0448501	0.2006117
BLose_v_BWin_L_Ins_r2	0.0003641	0.0014318	-0.0060852	-0.0049336	0.0006565	0.0012360	-0.0088326	-0.0062887	0.0030787	0.0013063	-0.0186075	-0.0177127	-0.0014950	-0.0099532	-0.0008615	-0.0202777	-0.0028511	-0.0027063	0.0083251	0.0069493	-0.0048918	-0.0032761	0.0157495	0.0123456	-0.0028515	-0.0024206	0.0387787	0.0326218	-0.0351787	0.1969232
BLose_v_BWin_R_Ins_r2	-0.0012158	0.0008081	-0.0074184	-0.0057624	-0.0017921	0.0006428	-0.0086037	-0.0049600	0.0028776	-0.0001931	-0.0160306	-0.0153662	-0.0002033	-0.0172335	0.0004937	-0.0309919	-0.0005667	-0.0006797	0.0075589	0.0094616	-0.0020770	-0.0008332	0.0131637	0.0183780	-0.0003570	-0.0013301	0.0326218	0.0493655	-0.0548790	0.2221835

11.2 AHRB

The covariance matrices for the [28] manifest variables for the primary AHRB dataset that has N observations: 97

ahrb_cov = cov(ahrb_df[,mod_vars])
ahrb_means = data.frame(means = colMeans(ahrb_df[,mod_vars]))
ahrb_sd = data.frame(sds = sapply(ahrb_df[,mod_vars], sd))
ahrb_dat = cbind(ahrb_cov, ahrb_means, ahrb_sd)

kable(ahrb_dat, booktabs = TRUE) %>%
  kable_styling(font_size = 12,position = 'center',html_font = "Times New Roman")

	AWin_v_Neut_L_NAc_r1	AWin_v_Neut_R_NAc_r1	AWin_v_Neut_L_NAc_r2	AWin_v_Neut_R_NAc_r2	BWin_v_Neut_L_NAc_r1	BWin_v_Neut_R_NAc_r1	BWin_v_Neut_L_NAc_r2	BWin_v_Neut_R_NAc_r2	BWin_v_BLose_L_NAc_r1	BWin_v_BLose_R_NAc_r1	BWin_v_BLose_L_NAc_r2	BWin_v_BLose_R_NAc_r2	AWin_v_Neut_R_Ins_r1	AWin_v_Neut_R_Ins_r2	BWin_v_Neut_R_Ins_r1	BWin_v_Neut_R_Ins_r2	ALose_v_Neut_L_Ins_r1	ALose_v_Neut_R_Ins_r1	ALose_v_Neut_L_Ins_r2	ALose_v_Neut_R_Ins_r2	BLose_v_Neut_L_Ins_r1	BLose_v_Neut_R_Ins_r1	BLose_v_Neut_L_Ins_r2	BLose_v_Neut_R_Ins_r2	BLose_v_BWin_L_Ins_r1	BLose_v_BWin_R_Ins_r1	BLose_v_BWin_L_Ins_r2	BLose_v_BWin_R_Ins_r2	means	sds
AWin_v_Neut_L_NAc_r1	0.0439544	0.0231727	-0.0012279	-0.0014998	0.0427961	0.0226606	-0.0006752	-0.0028637	0.0082361	0.0047335	-0.0017275	-0.0005411	0.0048915	-0.0013430	0.0027139	-0.0012670	0.0017386	0.0041057	-0.0044070	-0.0027817	-0.0006973	0.0041590	-0.0039596	-0.0027961	-0.0018067	0.0014517	-0.0025004	-0.0015289	0.0738454	0.2096531
AWin_v_Neut_R_NAc_r1	0.0231727	0.0508134	0.0010035	-0.0013565	0.0242770	0.0497329	0.0046295	-0.0000099	0.0050771	0.0143424	0.0109995	0.0087400	0.0082572	0.0041686	0.0081427	0.0045076	0.0029775	0.0079334	-0.0041267	-0.0000819	0.0006570	0.0075824	-0.0065458	-0.0004050	-0.0027629	-0.0005643	-0.0046026	-0.0049220	0.0833814	0.2254182
AWin_v_Neut_L_NAc_r2	-0.0012279	0.0010035	0.0391293	0.0175615	0.0034845	0.0040276	0.0462985	0.0254264	0.0020669	0.0011756	0.0176269	0.0090988	0.0008790	0.0045861	0.0015278	0.0092309	-0.0020467	-0.0013156	0.0031119	0.0050174	-0.0036621	-0.0038663	0.0039921	0.0052160	-0.0020740	-0.0054081	-0.0061449	-0.0040142	0.0894021	0.1978113
AWin_v_Neut_R_NAc_r2	-0.0014998	-0.0013565	0.0175615	0.0342875	-0.0030457	-0.0007087	0.0180744	0.0376288	-0.0052354	0.0020904	0.0069908	0.0145897	0.0026743	0.0084130	-0.0000421	0.0120272	-0.0006881	0.0003109	0.0009437	0.0073140	0.0008569	0.0007150	0.0008694	0.0053484	0.0014746	0.0007429	-0.0089105	-0.0066664	0.1032887	0.1851688
BWin_v_Neut_L_NAc_r1	0.0427961	0.0242770	0.0034845	-0.0030457	0.0543659	0.0327353	0.0075973	-0.0019674	0.0183644	0.0133913	0.0057282	-0.0028439	0.0072958	0.0023895	0.0065567	0.0045163	0.0042109	0.0063506	-0.0002223	0.0018492	0.0014372	0.0053810	-0.0010321	0.0005201	-0.0018093	-0.0011616	-0.0050494	-0.0039965	0.1189175	0.2331649
BWin_v_Neut_R_NAc_r1	0.0226606	0.0497329	0.0040276	-0.0007087	0.0327353	0.0692512	0.0088513	0.0035009	0.0188945	0.0352227	0.0134474	0.0067874	0.0086717	0.0078699	0.0118814	0.0077917	0.0036520	0.0096485	-0.0005358	0.0046956	0.0004535	0.0081835	-0.0036543	0.0027452	-0.0038971	-0.0036952	-0.0035933	-0.0050512	0.1297216	0.2631563
BWin_v_Neut_L_NAc_r2	-0.0006752	0.0046295	0.0462985	0.0180744	0.0075973	0.0088513	0.0708309	0.0332630	0.0018056	0.0044710	0.0365469	0.0141814	0.0047388	0.0048856	0.0047564	0.0109829	-0.0001427	0.0021266	0.0027485	0.0072719	-0.0025482	-0.0018478	0.0046005	0.0096988	-0.0034352	-0.0066167	-0.0056197	-0.0012849	0.1279588	0.2661407
BWin_v_Neut_R_NAc_r2	-0.0028637	-0.0000099	0.0254264	0.0376288	-0.0019674	0.0035009	0.0332630	0.0562835	-0.0029165	0.0032632	0.0154123	0.0299325	0.0059215	0.0106530	0.0014170	0.0162120	0.0001430	0.0024472	0.0021313	0.0091878	0.0013241	0.0032831	0.0015844	0.0066770	0.0023282	0.0018577	-0.0131049	-0.0095098	0.1723505	0.2372415
BWin_v_BLose_L_NAc_r1	0.0082361	0.0050771	0.0020669	-0.0052354	0.0183644	0.0188945	0.0018056	-0.0029165	0.0540467	0.0315259	-0.0077489	-0.0057875	0.0032174	0.0023890	0.0074011	0.0042467	0.0022096	0.0030871	-0.0016181	-0.0012116	0.0002616	0.0018486	-0.0021138	-0.0024280	-0.0052616	-0.0055385	-0.0027881	-0.0066563	0.0672474	0.2324794
BWin_v_BLose_R_NAc_r1	0.0047335	0.0143424	0.0011756	0.0020904	0.0133913	0.0352227	0.0044710	0.0032632	0.0315259	0.0540276	0.0025160	0.0011255	0.0032398	0.0069821	0.0074258	0.0088249	0.0045253	0.0055177	0.0031251	0.0053192	0.0022466	0.0038225	0.0047434	0.0044971	-0.0044251	-0.0036028	-0.0008131	-0.0043148	0.0671134	0.2324384
BWin_v_BLose_L_NAc_r2	-0.0017275	0.0109995	0.0176269	0.0069908	0.0057282	0.0134474	0.0365469	0.0154123	-0.0077489	0.0025160	0.0635716	0.0266915	-0.0000213	0.0071079	0.0008686	0.0105180	-0.0006599	0.0003334	-0.0007942	0.0048493	-0.0027193	-0.0024611	-0.0016632	0.0076620	-0.0033998	-0.0033256	-0.0037755	-0.0028563	0.0783608	0.2521341
BWin_v_BLose_R_NAc_r2	-0.0005411	0.0087400	0.0090988	0.0145897	-0.0028439	0.0067874	0.0141814	0.0299325	-0.0057875	0.0011255	0.0266915	0.0566720	0.0005638	0.0080790	0.0001107	0.0105667	-0.0005193	-0.0003602	-0.0011989	0.0029459	0.0002799	0.0011567	-0.0024053	0.0032608	-0.0010881	0.0010504	-0.0070446	-0.0072878	0.0992062	0.2380589
AWin_v_Neut_R_Ins_r1	0.0048915	0.0082572	0.0008790	0.0026743	0.0072958	0.0086717	0.0047388	0.0059215	0.0032174	0.0032398	-0.0000213	0.0005638	0.0194581	0.0043224	0.0200610	0.0056087	0.0107573	0.0177479	0.0034658	0.0039207	0.0112640	0.0184013	0.0025081	0.0043464	-0.0002595	-0.0016655	-0.0043997	-0.0012590	0.0518351	0.1394923
AWin_v_Neut_R_Ins_r2	-0.0013430	0.0041686	0.0045861	0.0084130	0.0023895	0.0078699	0.0048856	0.0106530	0.0023890	0.0069821	0.0071079	0.0080790	0.0043224	0.0205839	0.0051826	0.0238547	0.0014902	0.0009336	0.0083532	0.0157404	0.0006890	0.0012467	0.0082476	0.0162367	-0.0038588	-0.0039361	-0.0061255	-0.0076155	0.0532577	0.1434711
BWin_v_Neut_R_Ins_r1	0.0027139	0.0081427	0.0015278	-0.0000421	0.0065567	0.0118814	0.0047564	0.0014170	0.0074011	0.0074258	0.0008686	0.0001107	0.0200610	0.0051826	0.0286225	0.0074930	0.0106088	0.0189233	0.0042405	0.0042226	0.0111192	0.0196190	0.0041830	0.0051836	-0.0051179	-0.0090099	-0.0039942	-0.0023050	0.0819588	0.1691819
BWin_v_Neut_R_Ins_r2	-0.0012670	0.0045076	0.0092309	0.0120272	0.0045163	0.0077917	0.0109829	0.0162120	0.0042467	0.0088249	0.0105180	0.0105667	0.0056087	0.0238547	0.0074930	0.0338847	0.0027427	0.0015079	0.0103036	0.0195937	0.0021089	0.0020823	0.0118537	0.0215943	-0.0039891	-0.0054100	-0.0105816	-0.0122812	0.0961134	0.1840779
ALose_v_Neut_L_Ins_r1	0.0017386	0.0029775	-0.0020467	-0.0006881	0.0042109	0.0036520	-0.0001427	0.0001430	0.0022096	0.0045253	-0.0006599	-0.0005193	0.0107573	0.0014902	0.0106088	0.0027427	0.0155818	0.0136345	0.0046061	0.0027949	0.0159456	0.0136934	0.0033494	0.0015844	0.0039155	0.0030790	-0.0011843	-0.0011524	0.0278351	0.1248271
ALose_v_Neut_R_Ins_r1	0.0041057	0.0079334	-0.0013156	0.0003109	0.0063506	0.0096485	0.0021266	0.0024472	0.0030871	0.0055177	0.0003334	-0.0003602	0.0177479	0.0009336	0.0189233	0.0015079	0.0136345	0.0253842	0.0038208	0.0024625	0.0144181	0.0264919	0.0026782	0.0023461	0.0047694	0.0075635	-0.0017271	0.0008341	0.0331340	0.1593243
ALose_v_Neut_L_Ins_r2	-0.0044070	-0.0041267	0.0031119	0.0009437	-0.0002223	-0.0005358	0.0027485	0.0021313	-0.0016181	0.0031251	-0.0007942	-0.0011989	0.0034658	0.0083532	0.0042405	0.0103036	0.0046061	0.0038208	0.0157410	0.0129906	0.0044180	0.0043385	0.0154299	0.0129300	0.0004318	0.0000962	0.0018014	0.0026236	0.0366907	0.1254633
ALose_v_Neut_R_Ins_r2	-0.0027817	-0.0000819	0.0050174	0.0073140	0.0018492	0.0046956	0.0072719	0.0091878	-0.0012116	0.0053192	0.0048493	0.0029459	0.0039207	0.0157404	0.0042226	0.0195937	0.0027949	0.0024625	0.0129906	0.0232496	0.0013973	0.0034938	0.0131161	0.0238740	-0.0017777	-0.0007265	0.0008182	0.0042817	0.0399175	0.1524783
BLose_v_Neut_L_Ins_r1	-0.0006973	0.0006570	-0.0036621	0.0008569	0.0014372	0.0004535	-0.0025482	0.0013241	0.0002616	0.0022466	-0.0027193	0.0002799	0.0112640	0.0006890	0.0111192	0.0021089	0.0159456	0.0144181	0.0044180	0.0013973	0.0228457	0.0178959	0.0024177	-0.0001187	0.0101125	0.0067715	-0.0017670	-0.0022263	0.0485773	0.1511481
BLose_v_Neut_R_Ins_r1	0.0041590	0.0075824	-0.0038663	0.0007150	0.0053810	0.0081835	-0.0018478	0.0032831	0.0018486	0.0038225	-0.0024611	0.0011567	0.0184013	0.0012467	0.0196190	0.0020823	0.0136934	0.0264919	0.0043385	0.0034938	0.0178959	0.0335778	0.0027592	0.0031367	0.0080788	0.0139537	-0.0011956	0.0010464	0.0615567	0.1832424
BLose_v_Neut_L_Ins_r2	-0.0039596	-0.0065458	0.0039921	0.0008694	-0.0010321	-0.0036543	0.0046005	0.0015844	-0.0021138	0.0047434	-0.0016632	-0.0024053	0.0025081	0.0082476	0.0041830	0.0118537	0.0033494	0.0026782	0.0154299	0.0131161	0.0024177	0.0027592	0.0208023	0.0166487	-0.0012510	-0.0014301	0.0051803	0.0047940	0.0503093	0.1442299
BLose_v_Neut_R_Ins_r2	-0.0027961	-0.0004050	0.0052160	0.0053484	0.0005201	0.0027452	0.0096988	0.0066770	-0.0024280	0.0044971	0.0076620	0.0032608	0.0043464	0.0162367	0.0051836	0.0215943	0.0015844	0.0023461	0.0129300	0.0238740	-0.0001187	0.0031367	0.0166487	0.0323038	-0.0033062	-0.0020467	0.0041202	0.0107055	0.0719278	0.1797325
BLose_v_BWin_L_Ins_r1	-0.0018067	-0.0027629	-0.0020740	0.0014746	-0.0018093	-0.0038971	-0.0034352	0.0023282	-0.0052616	-0.0044251	-0.0033998	-0.0010881	-0.0002595	-0.0038588	-0.0051179	-0.0039891	0.0039155	0.0047694	0.0004318	-0.0017777	0.0101125	0.0080788	-0.0012510	-0.0033062	0.0208298	0.0131922	0.0004069	0.0006772	-0.0292784	0.1443254
BLose_v_BWin_R_Ins_r1	0.0014517	-0.0005643	-0.0054081	0.0007429	-0.0011616	-0.0036952	-0.0066167	0.0018577	-0.0055385	-0.0036028	-0.0033256	0.0010504	-0.0016655	-0.0039361	-0.0090099	-0.0054100	0.0030790	0.0075635	0.0000962	-0.0007265	0.0067715	0.0139537	-0.0014301	-0.0020467	0.0131922	0.0229649	0.0027973	0.0033509	-0.0203918	0.1515418
BLose_v_BWin_L_Ins_r2	-0.0025004	-0.0046026	-0.0061449	-0.0089105	-0.0050494	-0.0035933	-0.0056197	-0.0131049	-0.0027881	-0.0008131	-0.0037755	-0.0070446	-0.0043997	-0.0061255	-0.0039942	-0.0105816	-0.0011843	-0.0017271	0.0018014	0.0008182	-0.0017670	-0.0011956	0.0051803	0.0041202	0.0004069	0.0027973	0.0188771	0.0146872	-0.0245876	0.1373940
BLose_v_BWin_R_Ins_r2	-0.0015289	-0.0049220	-0.0040142	-0.0066664	-0.0039965	-0.0050512	-0.0012849	-0.0095098	-0.0066563	-0.0043148	-0.0028563	-0.0072878	-0.0012590	-0.0076155	-0.0023050	-0.0122812	-0.0011524	0.0008341	0.0026236	0.0042817	-0.0022263	0.0010464	0.0047940	0.0107055	0.0006772	0.0033509	0.0146872	0.0229739	-0.0241959	0.1515715

11.3 MLS

The covariance matrices for the [28] manifest variables for the MLS dataset that has N observations: 112

mls_cov = cov(mls_df[,mod_vars])
mls_means = data.frame(means = colMeans(mls_df[,mod_vars]))
mls_sd = data.frame(sds = sapply(mls_df[,mod_vars], sd))
mls_dat = cbind(mls_cov, mls_means, mls_sd)

kable(mls_dat, booktabs = TRUE) %>%
  kable_styling(font_size = 12,position = 'center',html_font = "Times New Roman")

	AWin_v_Neut_L_NAc_r1	AWin_v_Neut_R_NAc_r1	AWin_v_Neut_L_NAc_r2	AWin_v_Neut_R_NAc_r2	BWin_v_Neut_L_NAc_r1	BWin_v_Neut_R_NAc_r1	BWin_v_Neut_L_NAc_r2	BWin_v_Neut_R_NAc_r2	BWin_v_BLose_L_NAc_r1	BWin_v_BLose_R_NAc_r1	BWin_v_BLose_L_NAc_r2	BWin_v_BLose_R_NAc_r2	AWin_v_Neut_R_Ins_r1	AWin_v_Neut_R_Ins_r2	BWin_v_Neut_R_Ins_r1	BWin_v_Neut_R_Ins_r2	ALose_v_Neut_L_Ins_r1	ALose_v_Neut_R_Ins_r1	ALose_v_Neut_L_Ins_r2	ALose_v_Neut_R_Ins_r2	BLose_v_Neut_L_Ins_r1	BLose_v_Neut_R_Ins_r1	BLose_v_Neut_L_Ins_r2	BLose_v_Neut_R_Ins_r2	BLose_v_BWin_L_Ins_r1	BLose_v_BWin_R_Ins_r1	BLose_v_BWin_L_Ins_r2	BLose_v_BWin_R_Ins_r2	means	sds
AWin_v_Neut_L_NAc_r1	0.0491204	0.0288406	0.0084722	0.0038482	0.0564405	0.0361686	0.0145900	0.0079484	0.0271438	0.0187978	0.0053166	-0.0006767	-0.0005056	-0.0024722	-0.0015988	0.0000601	0.0048133	0.0043430	0.0011388	0.0068385	0.0054048	0.0051195	-0.0022368	0.0036398	-0.0010804	0.0067201	-0.0031756	0.0035899	0.2048661	0.2216312
AWin_v_Neut_R_NAc_r1	0.0288406	0.0432248	0.0043271	0.0063984	0.0336198	0.0488458	0.0108478	0.0105877	0.0177600	0.0262422	0.0072293	0.0047192	-0.0003989	-0.0008596	-0.0010357	0.0002795	0.0040452	0.0038148	0.0035807	0.0033290	0.0051003	0.0059562	0.0007548	0.0017914	-0.0004601	0.0069897	-0.0045633	0.0015015	0.2351339	0.2079057
AWin_v_Neut_L_NAc_r2	0.0084722	0.0043271	0.0480330	0.0317278	0.0120043	0.0054968	0.0494001	0.0345287	0.0017204	-0.0049508	0.0152001	0.0086996	0.0020141	0.0048539	0.0062170	0.0075308	0.0014567	0.0059615	0.0031975	0.0056174	0.0013427	0.0087950	0.0012006	0.0055729	0.0028322	0.0025836	-0.0080889	-0.0019693	0.1544643	0.2191644
AWin_v_Neut_R_NAc_r2	0.0038482	0.0063984	0.0317278	0.0497319	0.0031896	0.0060872	0.0318929	0.0503157	-0.0057873	-0.0065786	0.0028680	0.0098142	0.0038236	0.0055847	0.0077961	0.0089303	0.0065054	0.0061710	0.0018554	0.0042661	0.0072119	0.0099454	0.0018834	0.0069418	0.0017205	0.0021624	-0.0085074	-0.0020012	0.1506786	0.2230066
BWin_v_Neut_L_NAc_r1	0.0564405	0.0336198	0.0120043	0.0031896	0.0768879	0.0494858	0.0210702	0.0081760	0.0450555	0.0321798	0.0073458	-0.0037970	-0.0007197	-0.0025890	-0.0010558	0.0002287	0.0079270	0.0073451	0.0015774	0.0081018	0.0093821	0.0087410	-0.0015238	0.0053261	0.0023414	0.0098032	-0.0030025	0.0051199	0.2916518	0.2772867
BWin_v_Neut_R_NAc_r1	0.0361686	0.0488458	0.0054968	0.0060872	0.0494858	0.0667879	0.0144228	0.0115879	0.0305954	0.0441696	0.0087662	0.0040927	-0.0028896	0.0004579	-0.0019724	0.0022138	0.0051440	0.0049552	0.0063062	0.0061128	0.0065381	0.0075778	0.0019556	0.0037147	0.0021079	0.0095570	-0.0070892	0.0015004	0.3206071	0.2584336
BWin_v_Neut_L_NAc_r2	0.0145900	0.0108478	0.0494001	0.0318929	0.0210702	0.0144228	0.0632178	0.0431710	0.0062837	0.0012417	0.0247837	0.0159788	0.0034309	0.0066854	0.0076268	0.0102156	0.0052003	0.0084502	0.0058673	0.0084837	0.0051890	0.0119448	0.0033894	0.0081085	0.0049342	0.0043284	-0.0097079	-0.0021183	0.2337679	0.2514315
BWin_v_Neut_R_NAc_r2	0.0079484	0.0105877	0.0345287	0.0503157	0.0081760	0.0115879	0.0431710	0.0656961	-0.0049597	-0.0041894	0.0093006	0.0243163	0.0019942	0.0078964	0.0054559	0.0133351	0.0087562	0.0060609	0.0045183	0.0073821	0.0093781	0.0095437	0.0033297	0.0102595	0.0036157	0.0041007	-0.0090032	-0.0030897	0.2461875	0.2563126
BWin_v_BLose_L_NAc_r1	0.0271438	0.0177600	0.0017204	-0.0057873	0.0450555	0.0305954	0.0062837	-0.0049597	0.0647933	0.0426521	0.0070136	-0.0077156	-0.0015982	-0.0017000	-0.0006512	0.0002987	0.0015955	0.0031614	0.0023308	0.0042369	-0.0008183	0.0019465	0.0016301	0.0034021	-0.0048854	0.0026014	-0.0031164	0.0031328	0.1565536	0.2545454
BWin_v_BLose_R_NAc_r1	0.0187978	0.0262422	-0.0049508	-0.0065786	0.0321798	0.0441696	0.0012417	-0.0041894	0.0426521	0.0699709	0.0036278	0.0004384	-0.0001417	0.0019662	0.0003212	0.0025503	0.0005495	0.0034936	0.0051761	0.0047767	-0.0022787	0.0017684	0.0034586	0.0030124	-0.0028666	0.0014407	-0.0002491	0.0004789	0.1337589	0.2645201
BWin_v_BLose_L_NAc_r2	0.0053166	0.0072293	0.0152001	0.0028680	0.0073458	0.0087662	0.0247837	0.0093006	0.0070136	0.0036278	0.0452735	0.0289975	-0.0030565	0.0038220	-0.0009229	0.0025703	-0.0023924	-0.0027728	0.0025923	0.0011957	-0.0030494	-0.0023233	-0.0003860	-0.0043997	-0.0011322	-0.0014081	-0.0087927	-0.0069793	0.1091696	0.2127757
BWin_v_BLose_R_NAc_r2	-0.0006767	0.0047192	0.0086996	0.0098142	-0.0037970	0.0040927	0.0159788	0.0243163	-0.0077156	0.0004384	0.0289975	0.0585021	-0.0023893	0.0021802	0.0002520	0.0004865	0.0040214	0.0024590	0.0026501	-0.0007675	0.0042905	0.0030737	-0.0009557	-0.0052316	0.0054127	0.0028193	-0.0045987	-0.0057315	0.1128661	0.2418720
AWin_v_Neut_R_Ins_r1	-0.0005056	-0.0003989	0.0020141	0.0038236	-0.0007197	-0.0028896	0.0034309	0.0019942	-0.0015982	-0.0001417	-0.0030565	-0.0023893	0.0247935	0.0019229	0.0257559	0.0027260	0.0104119	0.0167879	0.0026999	0.0045621	0.0118655	0.0177437	0.0038792	0.0052455	-0.0026167	-0.0080094	0.0037302	0.0025171	0.0453661	0.1574596
AWin_v_Neut_R_Ins_r2	-0.0024722	-0.0008596	0.0048539	0.0055847	-0.0025890	0.0004579	0.0066854	0.0078964	-0.0017000	0.0019662	0.0038220	0.0021802	0.0019229	0.0214717	0.0033867	0.0235572	0.0028064	0.0016535	0.0071716	0.0116004	0.0028786	0.0009267	0.0066476	0.0106209	0.0016199	-0.0024551	-0.0073532	-0.0129441	0.0303571	0.1465323
BWin_v_Neut_R_Ins_r1	-0.0015988	-0.0010357	0.0062170	0.0077961	-0.0010558	-0.0019724	0.0076268	0.0054559	-0.0006512	0.0003212	-0.0009229	0.0002520	0.0257559	0.0033867	0.0352719	0.0050600	0.0126971	0.0200732	0.0047395	0.0072194	0.0143996	0.0210873	0.0044401	0.0082350	-0.0045040	-0.0141785	0.0002230	0.0031649	0.0727946	0.1878081
BWin_v_Neut_R_Ins_r2	0.0000601	0.0002795	0.0075308	0.0089303	0.0002287	0.0022138	0.0102156	0.0133351	0.0002987	0.0025503	0.0025703	0.0004865	0.0027260	0.0235572	0.0050600	0.0339695	0.0029443	0.0009380	0.0063303	0.0138545	0.0039099	0.0000850	0.0058566	0.0146103	0.0010995	-0.0049708	-0.0119096	-0.0193631	0.0725536	0.1843080
ALose_v_Neut_L_Ins_r1	0.0048133	0.0040452	0.0014567	0.0065054	0.0079270	0.0051440	0.0052003	0.0087562	0.0015955	0.0005495	-0.0023924	0.0040214	0.0104119	0.0028064	0.0126971	0.0029443	0.0303021	0.0173015	0.0007686	0.0031018	0.0346867	0.0196098	0.0015165	0.0047259	0.0157189	0.0069138	0.0001506	0.0017711	-0.0021518	0.1740749
ALose_v_Neut_R_Ins_r1	0.0043430	0.0038148	0.0059615	0.0061710	0.0073451	0.0049552	0.0084502	0.0060609	0.0031614	0.0034936	-0.0027728	0.0024590	0.0167879	0.0016535	0.0200732	0.0009380	0.0173015	0.0283940	0.0021297	0.0038009	0.0211692	0.0293497	0.0018766	0.0054019	0.0110574	0.0092800	-0.0004940	0.0044518	0.0321071	0.1685052
ALose_v_Neut_L_Ins_r2	0.0011388	0.0035807	0.0031975	0.0018554	0.0015774	0.0063062	0.0058673	0.0045183	0.0023308	0.0051761	0.0025923	0.0026501	0.0026999	0.0071716	0.0047395	0.0063303	0.0007686	0.0021297	0.0180299	0.0088972	0.0008868	0.0020224	0.0164219	0.0073534	-0.0021394	-0.0027088	0.0011010	0.0010225	-0.0074286	0.1342753
ALose_v_Neut_R_Ins_r2	0.0068385	0.0033290	0.0056174	0.0042661	0.0081018	0.0061128	0.0084837	0.0073821	0.0042369	0.0047767	0.0011957	-0.0007675	0.0045621	0.0116004	0.0072194	0.0138545	0.0031018	0.0038009	0.0088972	0.0198080	0.0034983	0.0040973	0.0058917	0.0179872	-0.0001470	-0.0031063	-0.0037361	0.0041311	0.0114286	0.1407410
BLose_v_Neut_L_Ins_r1	0.0054048	0.0051003	0.0013427	0.0072119	0.0093821	0.0065381	0.0051890	0.0093781	-0.0008183	-0.0022787	-0.0030494	0.0042905	0.0118655	0.0028786	0.0143996	0.0039099	0.0346867	0.0211692	0.0008868	0.0034983	0.0476872	0.0289892	0.0020263	0.0060190	0.0260205	0.0145865	-0.0002832	0.0020914	0.0406786	0.2183740
BLose_v_Neut_R_Ins_r1	0.0051195	0.0059562	0.0087950	0.0099454	0.0087410	0.0075778	0.0119448	0.0095437	0.0019465	0.0017684	-0.0023233	0.0030737	0.0177437	0.0009267	0.0210873	0.0000850	0.0196098	0.0293497	0.0020224	0.0040973	0.0289892	0.0423664	0.0012033	0.0054621	0.0162897	0.0212854	-0.0015316	0.0053639	0.0641518	0.2058310
BLose_v_Neut_L_Ins_r2	-0.0022368	0.0007548	0.0012006	0.0018834	-0.0015238	0.0019556	0.0033894	0.0033297	0.0016301	0.0034586	-0.0003860	-0.0009557	0.0038792	0.0066476	0.0044401	0.0058566	0.0015165	0.0018766	0.0164219	0.0058917	0.0020263	0.0012033	0.0230317	0.0092124	0.0003896	-0.0032312	0.0074545	0.0033628	0.0132857	0.1517620
BLose_v_Neut_R_Ins_r2	0.0036398	0.0017914	0.0055729	0.0069418	0.0053261	0.0037147	0.0081085	0.0102595	0.0034021	0.0030124	-0.0043997	-0.0052316	0.0052455	0.0106209	0.0082350	0.0146103	0.0047259	0.0054019	0.0073534	0.0179872	0.0060190	0.0054621	0.0092124	0.0254363	0.0018659	-0.0027626	-0.0004160	0.0108248	0.0382411	0.1594878
BLose_v_BWin_L_Ins_r1	-0.0010804	-0.0004601	0.0028322	0.0017205	0.0023414	0.0021079	0.0049342	0.0036157	-0.0048854	-0.0028666	-0.0011322	0.0054127	-0.0026167	0.0016199	-0.0045040	0.0010995	0.0157189	0.0110574	-0.0021394	-0.0001470	0.0260205	0.0162897	0.0003896	0.0018659	0.0360546	0.0207933	-0.0004443	0.0007495	-0.0175446	0.1898804
BLose_v_BWin_R_Ins_r1	0.0067201	0.0069897	0.0025836	0.0021624	0.0098032	0.0095570	0.0043284	0.0041007	0.0026014	0.0014407	-0.0014081	0.0028193	-0.0080094	-0.0024551	-0.0141785	-0.0049708	0.0069138	0.0092800	-0.0027088	-0.0031063	0.0145865	0.0212854	-0.0032312	-0.0027626	0.0207933	0.0354643	-0.0017617	0.0022051	-0.0086250	0.1883198
BLose_v_BWin_L_Ins_r2	-0.0031756	-0.0045633	-0.0080889	-0.0085074	-0.0030025	-0.0070892	-0.0097079	-0.0090032	-0.0031164	-0.0002491	-0.0087927	-0.0045987	0.0037302	-0.0073532	0.0002230	-0.0119096	0.0001506	-0.0004940	0.0011010	-0.0037361	-0.0002832	-0.0015316	0.0074545	-0.0004160	-0.0004443	-0.0017617	0.0279993	0.0114987	-0.0231518	0.1673299
BLose_v_BWin_R_Ins_r2	0.0035899	0.0015015	-0.0019693	-0.0020012	0.0051199	0.0015004	-0.0021183	-0.0030897	0.0031328	0.0004789	-0.0069793	-0.0057315	0.0025171	-0.0129441	0.0031649	-0.0193631	0.0017711	0.0044518	0.0010225	0.0041311	0.0020914	0.0053639	0.0033628	0.0108248	0.0007495	0.0022051	0.0114987	0.0301907	-0.0343125	0.1737548